共查询到20条相似文献,搜索用时 15 毫秒
1.
Bonaventura Luca Calzola Elisa Carlini Elisabetta Ferretti Roberto 《Journal of scientific computing》2021,88(1):1-22
Journal of Scientific Computing - We analyse numerically the periodic problem and the initial boundary value problem of the Korteweg-de Vries equation and the Drindfeld–Sokolov–Wilson... 相似文献
2.
Using the weighted residual formulation we derive a-posteriori estimates for Discontinuous Galerkin approximations of second order elliptic problems in mixed form. We show that our approach allows to include in a unified way all the methods presented so far in the literature. 相似文献
3.
A residual type a posteriori error estimator is presented and analyzed for Weak Galerkin finite element methods for second order elliptic problems. The error estimator is proved to be efficient and reliable through two estimates, one from below and the other from above, in terms of an $H^1$ -equivalent norm for the exact error. Two numerical experiments are conducted to demonstrate the effectiveness of adaptive mesh refinement guided by this estimator. 相似文献
4.
In this paper, we develop a class of high order conservative semi-Lagrangian (SL) discontinuous Galerkin methods for solving multi-dimensional linear transport equations. The methods rely on a characteristic Galerkin weak formulation, leading to \(L^2\) stable discretizations for linear problems. Unlike many existing SL methods, the high order accuracy and mass conservation of the proposed methods are realized in a non-splitting manner. Thus, the detrimental splitting error, which is known to significantly contaminate long term transport simulations, will be not incurred. One key ingredient in the scheme formulation, borrowed from CSLAM (Lauritzen et al. in J Comput Phys 229(5):1401–1424, 2010), is the use of Green’s theorem which allows us to convert volume integrals into a set of line integrals. The resulting line integrals are much easier to approximate with high order accuracy, hence facilitating the implementation. Another novel ingredient is the construction of quadratic curves in approximating sides of upstream cell, leading to quadratic-curved quadrilateral upstream cells. Formal third order accuracy is obtained by such a construction. The desired positivity-preserving property is further attained by incorporating a high order bound-preserving filter. To assess the performance of the proposed methods, we test and compare the numerical schemes with a variety of configurations for solving several benchmark transport problems with both smooth and nonsmooth solutions. The efficiency and efficacy are numerically verified. 相似文献
5.
In this paper, we propose a structure‐preserving model reduction method for second‐order systems based on H2 optimal interpolation. In the iterative process of the proposed method, an algorithm is presented for selecting interpolation points in order to control the dimension of the reduced system. Result about error analysis of the interpolation points selection algorithm is obtained and the property of the new model reduction method is also given. Finally, three numerical examples are performed to illustrate the effectiveness of the new method. 相似文献
6.
The paper considers the iterative improvement algorithms, the efficiency of which substantially depends on the chosen parameters values. The problem of control of these parameters is formulated and discussed. We designed the modified algorithms where parameters are automatically adjusted at each iteration. The original and modified algorithms are applied to solve the problem of optimal control for the ecology-economic system. 相似文献
7.
《国际计算机数学杂志》2012,89(9):1001-1008
The discrete approximation to a second order boundary value problem by finite difference methods gives rise to a system with a coefficient matrix which is typically banded. Several articles discuss the solution of such systems. Here the efficient method is based on the idea of a system perturbation followed by corrections and is competitive with standard methods 相似文献
8.
A. Bermúdez L. Hervella-Nieto A. Prieto R. Rodríguez 《Archives of Computational Methods in Engineering》2010,17(1):77-107
The main goal of this work is to give a review of the Perfectly Matched Layer (PML) technique for time-harmonic problems.
Precisely, we focus our attention on problems stated in unbounded domains, which involve second order elliptic equations writing
in divergence form and, in particular, on the Helmholtz equation at low frequency regime. Firstly, the PML technique is introduced
by means of a simple porous model in one dimension. It is emphasized that an adequate choice of the so called complex absorbing
function in the PML yields to accurate numerical results. Then, in the two-dimensional case, the PML governing equation is
described for second order partial differential equations by using a smooth complex change of variables. Its mathematical
analysis and some particular examples are also included. Numerical drawbacks and optimal choice of the PML absorbing function
are studied in detail. In fact, theoretical and numerical analysis show the advantages of using non-integrable absorbing functions.
Finally, we present some relevant real life numerical simulations where the PML technique is widely and successfully used
although they are not covered by the standard theoretical framework. 相似文献
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A novel and simple numerical method for stiff convection-dominated problems is studied in presence of boundary or interior layers. A version of the spectral Chevyshev-collocation method enriched with the so-called corrector functions is investigated. The corrector functions here are designed to capture the stiffness of the layers (see the Appendix), and the proposed method does not rely on the adaptive grid points. The extensive numerical results demonstrate that the enriched spectral methods are very accurate with low computational cost. 相似文献
11.
Bernardo Cockburn Manuel A. Sánchez Chunguang Xiong 《Journal of scientific computing》2018,75(1):376-394
We show that two widely used Galerkin formulations for second-order elliptic problems provide approximations which are actually superclose, that is, their difference converges faster than the corresponding errors. In the framework of linear elasticity, the two formulations correspond to using either the stiffness tensor or its inverse the compliance tensor. We find sufficient conditions, for a wide class of methods (including mixed and discontinuous Galerkin methods), which guarantee a supercloseness result. For example, for the HDG\(_{k}\) method using polynomial approximations of degree \({k>0}\), we find that the difference of approximate fluxes superconverges with order \({k+2}\) and that the difference of the scalar approximations superconverges with order \({k+3}\). We provide numerical results verifying our theoretical results. 相似文献
12.
In this paper we consider the case of nonlinear convection-diffusion problems with a dominating convection term and we propose
exponential integrators based on the composition of exact pure convection flows. These methods can be applied to the numerical
integration of the considered PDEs in a semi-Lagrangian fashion. Semi-Lagrangian methods perform well on convection dominated
problems (Pironneau in Numer. Math. 38:309–332, 1982; Hockney and Eastwood in Computer simulations using particles. McGraw-Hill, New York, 1981; Rees and Morton in SIAM J. Sci. Stat. Comput. 12(3):547–572, 1991; Baines in Moving finite elements. Monographs on numerical analysis. Clarendon Press, Oxford, 1994).
In these methods linear convective terms can be integrated exactly by first computing the characteristics corresponding to the gridpoints of the adopted discretization, and then producing
the numerical approximation via an interpolation procedure. 相似文献
13.
生物视觉关于二阶运动的研究成果,为计算机视觉的发展提供新的理论支持和研究方向.本文深入分析二阶运动信号,按照信号调制的方式将其分为空间调制、时间调制、时空调制三类运动.利用基于相关模型的一阶运动感知系统及纹理捕获器加相关模型的二阶运动感知系统对各类二阶运动现象进行实验,计算结果支持生物视觉关于二阶运动是由非线性的感知系统加工的结论. 相似文献
14.
Temporal error bounds for the wave equation expressed on second order form are investigated. We show that, with appropriate choices of boundary conditions, the time and space derivatives of the error are bounded even for long times. No long time bound on the error itself is obtained, although numerical experiments indicate that a bound exists. 相似文献
15.
In this paper we shall present, for the convection-dominated Sobolev equations, the fully-discrete numerical scheme based
on the local discontinuous Galerkin (LDG) finite element method and the third-order explicitly total variation diminishing
Runge-Kutta (TVDRK3) time marching. A priori error estimate is obtained for any piecewise polynomials of degree at most k≥1, under the general spatial-temporal restriction. The bounded constant in error estimate is independent of the reciprocal
of the diffusion and dispersion coefficients, after removing the effect of smoothness of the exact solution. Finally some
numerical results are given to verify the presented conclusion. 相似文献
16.
Olivier Bokanowski Jochen Garcke Michael Griebel Irene Klompmaker 《Journal of scientific computing》2013,55(3):575-605
We propose a semi-Lagrangian scheme using a spatially adaptive sparse grid to deal with non-linear time-dependent Hamilton-Jacobi Bellman equations. We focus in particular on front propagation models in higher dimensions which are related to control problems. We test the numerical efficiency of the method on several benchmark problems up to space dimension d=8, and give evidence of convergence towards the exact viscosity solution. In addition, we study how the complexity and precision scale with the dimension of the problem. 相似文献
17.
Bustinza Rommel Gatica Gabriel N. Cockburn Bernardo 《Journal of scientific computing》2005,22(1-3):147-185
In this paper we present a new residual-based reliable a posteriori error estimator for the local discontinuous Galerkin approximations of linear and nonlinear diffusion problems in polygonal regions of R
2. Our analysis, which applies to convex and nonconvex domains, is based on Helmholtz decompositions of the error and a suitable auxiliary polynomial function interpolating the Dirichlet datum. Several examples confirming the reliability of the estimator and providing numerical evidences for its efficiency are given. Furthermore, the associated adaptive method, which considers meshes with and without hanging nodes, is shown to be much more efficient than a uniform refinement to compute the discrete solutions. In particular, the experiments illustrate the ability of the adaptive algorithm to localize the singularities of each problem.Mathematics Subject Classifications (1991). 65N30This revised version was published online in July 2005 with corrected volume and issue numbers. 相似文献
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Thirupathi Gudi Hari Shanker Gupta Neela Nataraj 《Journal of scientific computing》2013,54(1):177-199
Error analysis for a stable C 0 interior penalty method is derived for general fourth order problems on polygonal domains under minimal regularity assumptions on the exact solution. We prove that this method exhibits quasi-optimal order of convergence in the discrete H 2, H 1 and L 2 norms. L ?? norm error estimates are also discussed. Theoretical results are demonstrated by numerical experiments. 相似文献
20.
Sabine Le Borne 《Computing》2000,64(2):123-155
Multigrid methods with simple smoothers have been proven to be very successful for elliptic problems with no or only moderate
convection. In the presence of dominant convection or anisotropies as it might appear in equations of computational fluid
dynamics (e.g. in the Navier-Stokes equations), the convergence rate typically decreases. This is due to a weakened smoothing
property as well as to problems in the coarse grid correction.
In order to obtain a multigrid method that is robust for convection-dominated problems, we construct efficient smoothers that
obtain their favorable properties through an appropriate ordering of the unknowns. We propose several ordering techniques
that work on the graph associated with the (convective part of the) stiffness matrix. The ordering algorithms provide a numbering
together with a block structure which can be used for block iterative methods.
We provide numerical results for the Stokes equations with a convective term illustrating the improved convergence properties
of the multigrid algorithm when applied with an appropriate ordering of the unknowns.
Received July 12, 1999; revised October 1, 1999 相似文献