Profiling a decade of Information Systems Frontiers’ research

This article analyses the first 10 years of research published in the Information Systems Frontiers (ISF) from 1999 to 2008. The analysis of the published material includes examining variables such as most productive authors, citation analysis, universities associated with the most publications, geographic diversity, authors’ backgrounds and research methods. The keyword analysis suggests that ISF research has evolved from establishing concepts and domain of information systems (IS), technology and management to contemporary issues such as outsourcing, web services and security. The analysis presented in this paper has identified intellectually significant studies that have contributed to the development and accumulation of intellectual wealth of ISF. The analysis has also identified authors published in other journals whose work largely shaped and guided the researchers published in ISF. This research has implications for researchers, journal editors, and research institutions.

SEPIA: estimating selectivities of approximate string predicates in large Databases

Many database applications have the emerging need to support approximate queries that ask for strings that are similar to a given string, such as “name similar to smith” and “telephone number similar to 412-0964”. Query optimization needs the selectivity of such an approximate predicate, i.e., the fraction of records in the database that satisfy the condition. In this paper, we study the problem of estimating selectivities of approximate string predicates. We develop a novel technique, called Sepia, to solve the problem. Given a bag of strings, our technique groups the strings into clusters, builds a histogram structure for each cluster, and constructs a global histogram. It is based on the following intuition: given a query string q, a preselected string p in a cluster, and a string s in the cluster, based on the proximity between q and p, and the proximity between p and s, we can obtain a probability distribution from a global histogram about the similarity between q and s. We give a full specification of the technique using the edit distance metric. We study challenges in adopting this technique, including how to construct the histogram structures, how to use them to do selectivity estimation, and how to alleviate the effect of non-uniform errors in the estimation. We discuss how to extend the techniques to other similarity functions. Our extensive experiments on real data sets show that this technique can accurately estimate selectivities of approximate string predicates. A short version of this article appeared as [21] in the proceedings of the 31st International Conference on Very Large Data Bases (VLDB), August 30 – September 2, 2005, Trondheim, Norway. The source code of our algorithms is available at .     

On Approximate Jumbled Pattern Matching in Strings

Given a string s, the Parikh vector of s, denoted p(s), counts the multiplicity of each character in s. Searching for a match of a Parikh vector q in the text s requires finding a substring t of s with p(t)=q. This can be viewed as the task of finding a jumbled (permuted) version of a query pattern, hence the term Jumbled Pattern Matching. We present several algorithms for the approximate version of the problem: Given a string s and two Parikh vectors u,v (the query bounds), find all maximal occurrences in s of some Parikh vector q such that u≤q≤v. This definition encompasses several natural versions of approximate Parikh vector search. We present an algorithm solving this problem in sub-linear expected time using a wavelet tree of s, which can be computed in time O(n) in a preprocessing phase. We then discuss a Scrabble-like variation of the problem, in which a weight function on the letters of s is given and one has to find all occurrences in s of a substring t with maximum weight having Parikh vector p(t)≤v. For the case of a binary alphabet, we present an algorithm which solves the decision version of the Approximate Jumbled Pattern Matching problem in constant time, by indexing the string in subquadratic time.     

Characterizations of ordered semigroups in terms of (∈, ∈ ∨ q)-fuzzy interior ideals

In this paper, we give characterizations of ordered semigroups in terms of (∈, ∈ ∨q)-fuzzy interior ideals. We characterize different classes regular (resp. intra-regular, simple and semisimple) ordered semigroups in terms of (∈, ∈ ∨q)-fuzzy interior ideals (resp. (∈, ∈ ∨q)-fuzzy ideals). In this regard, we prove that in regular (resp. intra-regular and semisimple) ordered semigroups the concept of (∈, ∈ ∨q)-fuzzy ideals and (∈, ∈ ∨q)-fuzzy interior ideals coincide. We prove that an ordered semigroup S is simple if and only if it is (∈, ∈ ∨q)-fuzzy simple. We characterize intra-regular (resp. semisimple) ordered semigroups in terms of (∈, ∈ ∨q)-fuzzy ideals (resp. (∈, ∈ ∨q)-fuzzy interior ideals). Finally, we consider the concept of implication-based fuzzy interior ideals in an ordered semigroup, in particular, the implication operators in Lukasiewicz system of continuous-valued logic are discussed.     

Tight bounds for k-set agreement with limited-scope failure detectors

In a system with limited-scope failure detectors, there are q disjoint clusters of processes such that some correct process in each cluster is never suspected by any process in that cluster. The failure detector class S_x,q satisfies this property all the time, while ⋄S_x,q satisfies it eventually. This paper gives the first tight bounds for the k-set agreement task in asynchronous message-passing models augmented with failure detectors from either the S_x,q or ⋄S_x,q classes. For S_x,q, we show that any k-set agreement protocol that tolerates f failures must satisfy f < k + x − q if q < k and f < x otherwise, where x is the combined size of the q disjoint clusters if q < k (or the k largest, otherwise). This result establishes for the first time that the protocol of Mostèfaoui and Raynal for the S_x = S_x,1 failure detector is optimal. For ⋄S_x,q, we show that any k-set agreement protocol that tolerates f failures must satisfy if q < k and otherwise, where n + 1 is the total number of processes. We give a novel protocol that matches our lower bound, disproving a conjecture of Mostèfaoui and Raynal for the ⋄S_x = ⋄S_x,1 failure detector. Our lower bounds exploit techniques borrowed from Combinatorial Topology, demonstrating for the first time that this approach is applicable to models that encompass failure detectors.     

The trichotomy of HAVING queries on a probabilistic database

We study the evaluation of positive conjunctive queries with Boolean aggregate tests (similar to HAVING in SQL) on probabilistic databases. More precisely, we study conjunctive queries with predicate aggregates on probabilistic databases where the aggregation function is one of MIN, MAX, EXISTS, COUNT, SUM, AVG, or COUNT(DISTINCT) and the comparison function is one of =, ≠,≥,>,≤, or <. The complexity of evaluating a HAVING query depends on the aggregation function, α, and the comparison function, θ. In this paper, we establish a set of trichotomy results for conjunctive queries with HAVING predicates parametrized by (α, θ). For such queries (without self-joins), one of the following three statements is true: (1) the exact evaluation problem has P{\mathcal P} -time data complexity. In this case, we call the query safe. (2) The exact evaluation problem is \sharpP{{\sharp{\mathcal P}}} -hard, but the approximate evaluation problem has (randomized) P{{\mathcal P}} -time data complexity. More precisely, there exists an FPTRAS for the query. In this case, we call the query apx-safe. (3) The exact evaluation problem is \sharpP{{\sharp{\mathcal P}}} -hard, and the approximate evaluation problem is also hard. We call these queries hazardous. The precise definition of each class depends on the aggregate considered and the comparison function. Thus, we have queries that are (MAX,≥ )-safe, (COUNT,≤ )-apx-safe, (SUM,=)-hazardous, etc. Our trichotomy result is a significant extension of a previous dichotomy result for Boolean conjunctive queries into safe and not safe. For each of the three classes we present novel techniques. For safe queries, we describe an evaluation algorithm that uses random variables over semirings. For apx-safe queries, we describe an FPTRAS that relies on a novel algorithm for generating a random possible world satisfying a given condition. Finally, for hazardous queries we give novel proofs of hardness of approximation. The results for safe queries were previously announced (in Ré, C., Suciu, D. Efficient evaluation of. In: DBPL, pp. 186–200, 2007), but all other results are new.     

Determination of user interfaces in adaptive systems using a rough classification-based method

This paper presents a novel method for user classification in adaptive systems based on rough classification. Adaptive systems could be used in many areas, for example in a user interface construction or e-Learning environments for learning strategy selection. In this paper the adaptation of web-based system user interface is presented. The goal of rough user classification is to select the most essential attributes and their values that group together users who are very much alike concerning the system logic. In order to group users we exploit their usage data taken from the user model of the adaptive web-based system user interface. We presented three basic problems for attribute selection that generates the following partitions: that is included, that includes and that is the closest to the given partition. Ngoc Thanh Nguyen, Ph.D., D.Sc.: He currently works as an associate professor at the Faculty of Computer Science and Management, Wroclaw University of Technology in Poland. He received his diplomas of M.Sc, Ph.D. and D.Sc. in Computer Science in 1986, 1989 and 2002, respectively. Actually, he is working on intelligent technologies for conflict resolution and inconsistent knowledge processing and e-learning methods. His teaching interests consist of database systems and distributed systems. He is a co-editor of 4 special issues in international journals, author of 3 monographs, editor of one book and about 110 other publications (book chapters, journal and refereed conference papers). He is an associate editor of the following journals: “International Journal of Computer Science & Application”; “Journal of Information Knowledge System Management”; and “International Journal of Knowledge-Based & Intelligent Engineering Systems”. He is a member of societies: ACM, IFIP WG 7.2, ISAI, KES International, and WIC. Janusz Sobecki, Ph.D.: He is an Assistant Professor in Institute of Applied Informatics (IAI) at Wroclaw University of Technology (WUT). He received his M. Sc. in Computer Science from Faculty of Computer Science and Management at WUT in 1986 and Ph.D. in Computer Science from Faculty of Electronics at WUT in 1994. For 1986–1996 he was an Assistant at the Department of Information Systems (DIS) at WUT. For 1988–1996 he was also a head of the laboratory at DIS. For 1996–2004 he was an Assistant Professor in DIS and since fall of 2004 at IAI, both at WUT. His research interests include information retrieval, multimedia information systems, system usability and recommender systems. He is on the editorial board of New Generation Computing and was a co-editor of two journal special issues. He is a member of American Association of Machinery.     

An Efficient Scaling Algorithm for the Minimum Weight Bibranching Problem

Let G=(VG,AG) be a digraph and let S ⊔ T be a bipartition of VG. A bibranching is a subset B⊆AG such that for each node s∈S there exists a directed s–T path in B and, vice versa, for each node t∈T there exists a directed S–t path in B.     

Graph Spanners in the Streaming Model: An Experimental Study

This article reports the results of an extensive experimental analysis of efficient algorithms for computing graph spanners in the data streaming model, where an (α,β)-spanner of a graph G is a subgraph S⊆G such that for each pair of vertices the distance in S is at most α times the distance in G plus β. To the best of our knowledge, this is the first computational study of graph spanner algorithms in a streaming setting. We compare experimentally the randomized algorithms proposed by Baswana () and by Elkin (In: Proceedings of the 34th International Colloquium on Automata, Languages and Programming (ICALP 2007), Wroclaw, Poland, pp. 716–727, 9–13 July 2007) for general stretch factors with the deterministic algorithm presented by Ausiello et al. (In: Proceedings of the 15th Annual European Symposium on Algorithms (ESA 2007), Engineering and Applications Track, Eilat, Israel, 8–10 October 2007. LNCS, vol. 4698, pp. 605–617, 2007), designed for building small stretch spanners. All the algorithms we implemented work in a data streaming model where the input graph is given as a stream of edges in arbitrary order, and all of them need a single pass over the data. Differently from the algorithm in Ausiello et al., the algorithms in Baswana () and Elkin (In: Proceedings of the 34th International Colloquium on Automata, Languages and Programming (ICALP 2007), Wroclaw, Poland, pp. 716–727, 9–13 July 2007) need to know in advance the number of vertices in the graph. The results of our experimental investigation on several input families confirm that all these algorithms are very efficient in practice, finding spanners with stretch and size much smaller than the theoretical bounds and comparable to those obtainable by off-line algorithms. Moreover, our experimental findings confirm that small values of the stretch factor are the case of interest in practice, and that the algorithm by Ausiello et al. tends to produce spanners of better quality than the algorithms by Baswana and Elkin, while still using a comparable amount of time and space resources. Work partially supported by the Italian Ministry of University and Research under Project MAINSTREAM “Algorithms for Massive Information Structures and Data Streams”. A preliminary version of this paper was presented at the 15th Annual European Symposium on Algorithms (ESA 2007) 5.     

Solutions of Multi-dimensional Hyperbolic Systems of Conservation Laws by Square Entropy Condition Satisfying Discontinuous Galerkin Method

In this paper, we study formally high-order accurate discontinuous Galerkin methods on general arbitrary grid for multi-dimensional hyperbolic systems of conservation laws [Cockburn, B., and Shu, C.-W. (1989, Math. Comput. 52, 411–435, 1998, J. Comput. Phys. 141, 199–224); Cockburn et al. (1989, J. Comput. Phys. 84, 90–113; 1990, Math. Comput. 54, 545–581). We extend the notion of E-flux [Osher (1985) SIAM J. Numer. Anal. 22, 947–961] from scalar to system, and found that after flux splitting upwind flux [Cockburn et al. (1989) J. Comput. Phys. 84, 90–113] is a Riemann solver free E-flux for systems. Therefore, we are able to show that the discontinuous Galerkin methods satisfy a cell entropy inequality for square entropy (in semidiscrete sense) if the multi-dimensional systems are symmetric. Similar result [Jiang and Shu (1994) Math. Comput. 62, 531–538] was obtained for scalar equations in multi-dimensions. We also developed a second-order finite difference version of the discontinuous Galerkin methods. Numerical experiments have been obtained with excellent results.      

Strategic dependence on the IT resource and outsourcing: A test of the strategic control model

Using resource dependency theory (RDT), this research analyzes how organizations control their information technology resources to improve organizational performance. According to RDT, organizations must manage their dependency on external organizations and limit external dependencies when resources are considered critical. The current study proposes and tests a portion of a Strategic Control Model positing that managers seek to control important, strategic resources in order to create value for the firm and to avoid dependency on external entities. Utilizing a research design that captured extensive quantitative data on the control of IT functions and services, the research team gathered 5 years of data on 54 business units (BUs) in 27 global companies located in seven countries. Study examined the linkages of these 54 BUs to firm performance. Locating the Extent of Control within the firm in cases where the firm depends on IT as a strategic resource proves to be a good explanation for effective decisions leading to higher performance. Viewing IT as a strategic resource alone does not lead to positive business unit outcomes, but the moderating influence of Extent of Control is found to establish the complex statistical relationship with business unit performance. For these reasons, it is critical that a theoretically grounded firm-wide process for decisions on locating IT control is in place to capture business value.

Non-Linear Filtering and Limiting in High Order Methods for Ideal and Non-Ideal MHD

The adaptive nonlinear filtering and limiting in spatially high order schemes (Yee et al. J. Comput. Phys. 150, 199–238, (1999), Sjögreen and Yee, J. Scient. Comput. 20, 211–255, (2004)) for the compressible Euler and Navier–Stokes equations have been recently extended to the ideal and non-ideal magnetohydrodynamics (MHD) equations, (Sjögreen and Yee, (2003), Proceedings of the 16th AIAA/CFD conference, June 23–26, Orlando F1; Yee and Sjögreen (2003), Proceedings of the International Conference on High Performance Scientific Computing, March, 10–14, Honai, Vietnam; Yee and Sjögreen (2003), RIACS Technical Report TR03. 10, July, NASA Ames Research Center; Yee and Sjögreen (2004), Proceedings of the ICCF03, July 12–16, Toronto, Canada). The numerical dissipation control in these adaptive filter schemes consists of automatic detection of different flow features as distinct sensors to signal the appropriate type and amount of numerical dissipation/filter where needed and leave the rest of the region free from numerical dissipation contamination. The numerical dissipation considered consists of high order linear dissipation for the suppression of high frequency oscillation and the nonlinear dissipative portion of high-resolution shock-capturing methods for discontinuity capturing. The applicable nonlinear dissipative portion of high-resolution shock-capturing methods is very general. The objective of this paper is to investigate the performance of three commonly used types of discontinuity capturing nonlinear numerical dissipation for both the ideal and non-ideal MHD.     

Fuzzy <Emphasis Type="Italic">R</Emphasis>-subgroups with thresholds of near-rings and implication operators

Using the belongs to relation (∈) and quasi-coincidence with relation (q) between fuzzy points and fuzzy sets, the concept of (α, β)-fuzzy R-subgroup of a near-ring where α , β are any two of {∈, q, ∈∨q , ∈∧q} with α ≠ ∈∧q is introduced and related properties are investigated. We also introduce the notion of a fuzzy R-subgroup with thresholds which is a generalization of an ordinary fuzzy R-subgroup and an (∈, ∈∨q)-fuzzy R-subgroup. Finally, we give the definition of an implication-based fuzzy R-subgroup.     

Web data retrieval: solving spatial range queries using k-nearest neighbor searches

As Geographic Information Systems (GIS) technologies have evolved, more and more GIS applications and geospatial data are available on the web. Spatial objects in a given query range can be retrieved using spatial range query − one of the most widely used query types in GIS and spatial databases. However, it can be challenging to retrieve these data from various web applications where access to the data is only possible through restrictive web interfaces that support certain types of queries. A typical scenario is the existence of numerous business web sites that provide their branch locations through a limited “nearest location” web interface. For example, a chain restaurant’s web site such as McDonalds can be queried to find some of the closest locations of its branches to the user’s home address. However, even though the site has the location data of all restaurants in, for example, the state of California, it is difficult to retrieve the entire data set efficiently due to its restrictive web interface. Considering that k-Nearest Neighbor (k-NN) search is one of the most popular web interfaces in accessing spatial data on the web, this paper investigates the problem of retrieving geospatial data from the web for a given spatial range query using only k-NN searches. Based on the classification of k-NN interfaces on the web, we propose a set of range query algorithms to completely cover the rectangular shape of the query range (completeness) while minimizing the number of k-NN searches as possible (efficiency). We evaluated the efficiency of the proposed algorithms through statistical analysis and empirical experiments using both synthetic and real data sets.

ATR artificial brain project: 2004 progress report

This article presents the key assumptions and current status of the ATR Artificial Brain Project being undertaken to create Volitron, a device equipped with circuitry that enables the emergence of thought. Such thought would be recognized from Volitron's specific communication behaviors. The project consists of three complementary themes: psychodynamic architecture, brain-specific evolvable hardware, and the management of brain-building. The psychodynamic architecture is designed to develop automatically, driven by “pleasure” coming from discharges of tension gathered in special tension-accumulating devices. Tension-discharging patterns come first of all from the robot's interactions with its care giver/provider. For the dedicated hardware, we developed qcellular-automata (qCA), in which groups of uniform logic primitives (q-cells) serve as spike-train-processing units, as well as pulsed para-neural networks (PPNN) that can be evolved, using fuzzified signals and a genetic algorithm combined with hill climbing, and converted into qCA. The psychodynamic ideas were tested using three robots: Neko, equipped with a pleasure-driven associator, Miao, equipped with MemeStorms (a special working memory in which conflicting ideas fight for access to the long-term memory and actuators), and Miao+, whose brain is equipped with a growing neural network. This work was presented in part at the 9th International Symposium on Artificial Life and Robotics, Oita, Japan, January 28–30, 2004     

Effect of technological breakthroughs on electronic markets

Electronic markets have profoundly affected competition and market structures. Many authors have argued that electronic markets can promote competition and increase allocational efficiency, primarily by reducing buyer and seller search costs. However, conventional competitive models do not explain several phenomena we actually observe in electronic markets. Consequently, a variety of researchers have introduced complications to the basic competitive search model, including asymmetric information, branding and product differentiation, network effects, and agency considerations in order to explain e-commerce behavior. However, most previous studies neglect the fact that such characteristics may reflect underlying market evolution processes. Depending upon the evolutionary pattern of a market, the behavior and performance of markets differ. In this paper, we construct a model to examine e-commerce in the framework of dynamic market evolution. Using a system of replicator dynamics, we split a market into two distinct parts and show that the competition within the two segments will follow different, though interrelated evolutionary patterns. We supply the conditions for the existence of a unique global stable equilibrium in this dynamical system. Our model suggests that exogenous increases in online customers triggered by technological breakthrough often play more important roles than price differentials in determining the evolutionary path of a market. By emphasizing the short term disequilibrium along the market evolution path, our study complements the competitive equilibrium view of electronic market. Xiaotong Li is an Assistant Professor of MIS at the University of Alabama in Huntsville. His research has appeared in many major journals including Communications of the ACM, Marketing Science, IEEE Transactions and others. His current research interests are in applied game theory and the economics of IT. He has been invited to give research seminars at many major research universities. Dr. Li has been invited to referee research papers for many academic journals including MIS Quarterly, Information Systems Research, Marketing Science, Journal of MIS and Journal of AIS. He recently won the best paper award from IEEE Transaction on Engineering Management. Jatinder (Jeet) N. D. Gupta is currently Eminent Scholar of Management of Technology, Professor of Management Information Systems, Industrial and Systems Engineering and Engineering Management at the University of Alabama in Huntsville, Huntsville, Alabama. Most recently, he was Professor of Management, Information and Communication Sciences, and Industry and Technology at Ball State University, Muncie, Indiana. He holds a PhD in Industrial Engineering (with specialization in Production Management and Information Systems) from Texas Tech University. Co-author of a textbook in Operations Research, Dr. Gupta serves on the editorial boards of several national and international journals. Recipient of the Outstanding Faculty and Outstanding Researcher awards from Ball State University, he has published numerous papers in such journals as Journal of Management Information Systems, International Journal of Information Management, Operations Research, INFORMS Journal of Computing, Annals of Operations Research, and Mathematics of Operations Research. More recently, he served as a co-editor of several special issues including Design, Building and Evaluation of Intelligent DMSS of theJournal of Decision Systems, the Neural Networks in Business of Computers and Operations Research and books that include the Intelligent Decision Making Support Systems (i-DMSS): Foundations, Applications and Challengepublished by Springer-Verlag and Creating Knowledge-based Healthcare Organizations published by Idea Group Publishing. He is also the coeditor of the book: Managing E-Business published by Heidelberg Press, Heidelberg, Australia. His current research interests include e-Commerce, Supply Chain Management, Information and Decision Technologies, Scheduling, Planning and Control, Organizational Learning and Effectiveness, Systems Education, Knowledge Management, Information Security, and Enterprise Integration. Dr. Gupta has held elected and appointed positions in several academic and professional societies including the Association for Information Systems, Production and Operations Management Society (POMS), the Decision Sciences Institute (DSI), and the Information Resources Management Association (IRMA). James V. Koch is Board of Visitors Professor of Economics at Old Dominion University. Previously, he served as President of the University of Montana (1986–1990) and Old Dominion University (1990–2001). His recent published research has focused on: (1) the entrepreneurial behavior of college presidents and CEOs; and, (2) applied microeconomics. Dr. Koch has been a consultant to more than 75 corporations, foundations and legal firms.     

Optimal External Memory Planar Point Enclosure

In this paper we study the external memory planar point enclosure problem: Given N axis-parallel rectangles in the plane, construct a data structure on disk (an index) such that all K rectangles containing a query point can be reported I/O-efficiently. This problem has important applications in e.g. spatial and temporal databases, and is dual to the important and well-studied orthogonal range searching problem. Surprisingly, despite the fact that the problem can be solved optimally in internal memory with linear space and O(log N+K) query time, we show that one cannot construct a linear sized external memory point enclosure data structure that can be used to answer a query in O(log  _B N+K/B) I/Os, where B is the disk block size. To obtain this bound, Ω(N/B ^1−ε ) disk blocks are needed for some constant ε>0. With linear space, the best obtainable query bound is O(log ₂ N+K/B) if a linear output term O(K/B) is desired. To show this we prove a general lower bound on the tradeoff between the size of the data structure and its query cost. We also develop a family of structures with matching space and query bounds. An extended abstract of this paper appeared in Proceedings of the 12th European Symposium on Algorithms (ESA’04), Bergen, Norway, September 2004, pp. 40–52. L. Arge’s research was supported in part by the National Science Foundation through RI grant EIA–9972879, CAREER grant CCR–9984099, ITR grant EIA–0112849, and U.S.-Germany Cooperative Research Program grant INT–0129182, as well as by the US Army Research Office through grant W911NF-04-01-0278, by an Ole Roemer Scholarship from the Danish National Science Research Council, a NABIIT grant from the Danish Strategic Research Council and by the Danish National Research Foundation. V. Samoladas’ research was supported in part by a grant co-funded by the European Social Fund and National Resources-EPEAEK II-PYTHAGORAS. K. Yi’s research was supported in part by the National Science Foundation through ITR grant EIA–0112849, U.S.-Germany Cooperative Research Program grant INT–0129182, and Hong Kong Direct Allocation Grant (DAG07/08).     

Finite Volume Discretization and Multilevel Methods in Flow Problems

This article is intended as a preliminary report on the implementation of a finite volume multilevel scheme for the discretization of the incompressible Navier–Stokes equations. As is well known the use of staggered grids (e.g. MAC grids, Perić et al. Comput. Fluids, 16(4), 389–403, (1988)) is a serious impediment for the implementation of multilevel schemes in the context of finite differences. This difficulty is circumvented here by the use of a colocated finite volume discretization (Faure et al. (2004a) Submitted, Perić et al. Comput. Fluids, 16(4), 389–403, (1988)), for which the algebra of multilevel methods is much simpler than in the context of MAC type finite differences. The general ideas and the numerical simulations are presented in this article in the simplified context of a two-dimensional Burgers equations; the two-, and three-dimensional Navier–Stokes equations introducing new difficulties related to the incompressibility condition and the time discretization, will be considered elsewhere (see Faure et al. (2004a) Submitted and Faure et al. (2004b), in preparation).     

Superconvergence of Discontinuous Galerkin Methods for Convection-Diffusion Problems

Some discontinuous Galerkin methods for the linear convection-diffusion equation −ε u″+bu′=f are studied. Based on superconvergence properties of numerical fluxes at element nodes established in some earlier works, e.g., Celiker and Cockburn in Math. Comput. 76(257), 67–96, 2007, we identify superconvergence points for the approximations of u or q=u′. Our results are twofold: 1) For the minimal dissipation LDG method (we call it md-LDG in this paper) using polynomials of degree p, we prove that the leading terms of the discretization errors for u and q are proportional to the right Radau and left Radau polynomials of degree p+1, respectively. Consequently, the zeros of the right-Radau and left-Radau polynomials of degree p+1 are the superconvergence points of order p+2 for the discretization errors of the potential and of the gradient, respectively.