共查询到20条相似文献,搜索用时 31 毫秒
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Jun Cao 《Computers & Fluids》2005,34(8):991-1024
In this paper, we discuss how to improve the adaptive finite element simulation of compressible Navier-Stokes flow via a posteriori error estimate analysis. We use the moving space-time finite element method to globally discretize the time-dependent Navier-Stokes equations on a series of adapted meshes. The generalized compressible Stokes problem, which is the Stokes problem in its most generalized form, is presented and discussed. On the basis of the a posteriori error estimator for the generalized compressible Stokes problem, a numerical framework of a posteriori error estimation is established corresponding to the case of compressible Navier-Stokes equations. Guided by the a posteriori errors estimation, a combination of different mesh adaptive schemes involving simultaneous refinement/unrefinement and point-moving are applied to control the finite element mesh quality. Finally, a series of numerical experiments will be performed involving the compressible Stokes and Navier-Stokes flows around different aerodynamic shapes to prove the validity of our mesh adaptive algorithms. 相似文献
3.
A. Abdulle A. Nonnenmacher 《Computer Methods in Applied Mechanics and Engineering》2011,200(37-40):2710-2726
In this paper we present an a posteriori error analysis for elliptic homogenization problems discretized by the finite element heterogeneous multiscale method. Unlike standard finite element methods, our discretization scheme relies on macro- and microfinite elements. The desired macroscopic solution is obtained by a suitable averaging procedure based on microscopic data. As the macroscopic data (such as the macroscopic diffusion tensor) are not available beforehand, appropriate error indicators have to be defined for designing adaptive methods. We show that such indicators based only on the available macro- and microsolutions (used to compute the actual macrosolution) can be defined, allowing for a macroscopic mesh refinement strategy which is both reliable and efficient. The corresponding a posteriori estimates for the upper and lower bound are derived in the energy norm. In the case of a uniformly oscillating tensor, we recover the standard residual-based a posteriori error estimate for the finite element method applied to the homogenized problem. Numerical experiments confirm the efficiency and reliability of the adaptive multiscale method. 相似文献
4.
Huajie Chen Lianhua He Aihui Zhou 《Computer Methods in Applied Mechanics and Engineering》2011,200(21-22):1846-1865
In this paper, we study finite element approximations of a class of nonlinear eigenvalue problems arising from quantum physics. We derive both a priori and a posteriori finite element error estimates and obtain optimal convergence rates for both linear and quadratic finite element approximations. In particular, we analyze the convergence and complexity of an adaptive finite element method. In our analysis, we utilize certain relationship between the finite element eigenvalue problem and the associated finite element boundary value approximations. We also present several numerical examples in quantum physics that support our theory. 相似文献
5.
In this paper, we derive a posteriori error estimates of recovery type, and present the superconvergence analysis for the
finite element approximation of distributed convex optimal control problems. We provide a posteriori error estimates of recovery
type for both the control and the state approximation, which are generally equivalent. Under some stronger assumptions, they
are further shown to be asymptotically exact. Such estimates, which are apparently not available in the literature, can be
used to construct adaptive finite element approximation schemes and as a reliability bound for the control problems. Numerical
results demonstrating our theoretical results are also presented in this paper. 相似文献
6.
《Computer Methods in Applied Mechanics and Engineering》2005,194(2-5):499-510
In this paper we develop the a posteriori error estimation of mixed discontinuous Galerkin finite element approximations of the Maxwell operator. In particular, by employing suitable Helmholtz decompositions of the error, together with the conservation properties of the underlying method, computable upper bounds on the error, measured in terms of a natural (mesh-dependent) energy norm, are derived. Numerical experiments testing the performance of our a posteriori error bounds for problems with both smooth and singular analytical solutions are presented. 相似文献
7.
Consider the acoustic wave scattering by an impenetrable obstacle in two dimensions. The model is formulated as a boundary value problem for the Helmholtz equation with a transparent boundary condition. Based on a duality argument technique, an a posteriori error estimate is derived for the finite element method with the truncated Dirichlet-to-Neumann boundary operator. The a posteriori error estimate consists of the finite element approximation error and the truncation error of boundary operator which decays exponentially with respect to the truncation parameter. A new adaptive finite element algorithm is proposed for solving the acoustic obstacle scattering problem, where the truncation parameter is determined through the truncation error and the mesh elements for local refinements are marked through the finite element discretization error. Numerical experiments are presented to illustrate the competitive behavior of the proposed adaptive method. 相似文献
8.
Jun Cao 《Computers & Fluids》2005,34(8):972-990
The main goal of this paper is to study adaptive mesh techniques, using a posteriori error estimates, for the finite element solution of the Navier-Stokes equations modeling steady and unsteady flows of an incompressible viscous fluid. Among existing operator splitting techniques, the θ-scheme is used for time integration of the Navier-Stokes equations. Then, a posteriori error estimates, based on the solution of a local system for each triangular element, are presented in the framework of the generalized incompressible Stokes problem, followed by its practical application to the case of incompressible Navier-Stokes problem. Hierarchical mesh adaptive techniques are developed in response to the a posteriori error estimation. Numerical simulations of viscous flows associated with selected geometries are performed and discussed to demonstrate the accuracy and efficiency of our methodology. 相似文献
9.
In this paper, we study the adaptive finite element approximation for a constrained optimal control problem with both pointwise and integral control constraints. We first obtain the explicit solutions for the variational inequalities both in the continuous and discrete cases. Then a priori error estimates are established, and furthermore equivalent a posteriori error estimators are derived for both the state and the control approximation, which can be used to guide the mesh refinement for an adaptive multi-mesh finite element scheme. The a posteriori error estimators are implemented and tested with promising numerical results. 相似文献
10.
In this note, we extend our studies on finite element Galerkin schemes for elliptic variational inequalities of first to the
one of second kind. Especially we perform the corresponding a posteriori error analysis for a simple friction problem and
a model flow of a Bingham fluid. 相似文献
11.
We consider the problem of adaptive error control in the finite element method including the error resulting from, inexact solution of the discrete equations. We prove a posteriori error estimates for a prototype elliptic model problem discretized by the finite element with a canomical multigrid algorithm. The proofs are based on a combination of so-called strong stability and, the orthogonality inherent in both the finite element method can the multigrid algorithm. 相似文献
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发展型对流占优扩散方程的FD-SD法的后验误差估计及空间网格调节技术 总被引:4,自引:0,他引:4
0.引言 流线扩散法(streamline diffusion method,简称 SD法)是由Hughes和 Brooks在1980年前后提出的一种数值求解对流占优扩散问题的新型有限元算法.随后,Johnson和 Navert把SD法推广到发展型对流扩散问题.这一方法因其兼具良好的数值稳定性和高阶精度,近年来在理论与实践方面都得到了很大发展. 对于发展型对流扩散问题的SD法均采用时空有限元,即把时间、空间同等对待,这样做虽然使关于时间、空间的精度很好地统一起来,但与传统的有限元相比,由于维数增加,计… 相似文献
13.
In this paper, we study adaptive finite element approximation schemes for a constrained optimal control problem. We derive
the equivalent a posteriori error estimators for both the state and the control approximation, which particularly suit an
adaptive multi-mesh finite element scheme. The error estimators are then implemented and tested with promising numerical results. 相似文献
14.
In this paper, we study the a posteriori error estimates of two-grid finite volume element method for second-order nonlinear elliptic equations. We derive the residual-based a posteriori error estimator and prove the computable upper and lower bounds on the error in -norm. The a posteriori error estimator can be used to assess the accuracy of the two-grid finite volume element solutions in practical applications. Numerical examples are provided to illustrate the performance of the proposed estimator. 相似文献
15.
Vladislav Pimanov Ivan Oseledets 《Structural and Multidisciplinary Optimization》2018,58(4):1619-1632
In our work, we consider the classical density-based approach to the topology optimization. We propose to modify the discretized cost functional using a posteriori error estimator for the finite element method. It can be regarded as a new technique to prevent checkerboards. It also provides higher regularity of solutions and robustness of results. 相似文献
16.
Johan Hoffman Johan Jansson Rodrigo Vilela De Abreu 《Computer Methods in Applied Mechanics and Engineering》2011,200(37-40):2758-2767
In this paper we first review our recent work on a new framework for adaptive turbulence simulation: we model turbulence by weak solutions to the Navier–Stokes equations that are wellposed with respect to mean value output in the form of functionals, and we use an adaptive finite element method to compute approximations with a posteriori error control based on the error in the functional output. We then derive a local energy estimate for a particular finite element method, which we connect to related work on dissipative weak Euler solutions with kinetic energy dissipation due to lack of local smoothness of the weak solutions. The ideas are illustrated by numerical results, where we observe a law of finite dissipation with respect to a decreasing mesh size. 相似文献
17.
Qingsong Zou 《Journal of scientific computing》2013,54(1):77-96
We present and analyze a novel hierarchical a posteriori error estimate for elliptic obstacle problems. The main result is that the energy norm of the finite element approximate error is, up to some extra oscillation term, equivalent to an appropriate hierarchical estimator. The proof is based upon some new observations on efficiency and some technical tools deriving from a previous work (Zou et al. in Numer. Math. 117:653?C677, 2011). Moreover, we present an equivalence between the energy norm and the energy functional of the finite element approximate error. Several numerical experiments validate our theoretical findings. 相似文献
18.
A new gradient recovery technique SCR (Superconvergent Cluster Recovery) is proposed and analyzed for finite element methods.
A linear polynomial approximation is obtained by a least-squares fitting to the finite element solution at certain sample
points, which in turn gives the recovered gradient at recovering points. Compared with similar techniques such as SPR and
PPR, our approach is cheaper and efficient, while having same or even better accuracy. In additional, it can be used as an
a posteriori error estimator, which is relatively simple to implement, cheap in terms of storage and computational cost for
adaptive algorithms. We present some numerical examples illustrating the effectiveness of our recovery procedure. 相似文献
19.
Some a Posteriori Error Estimators for p-Laplacian Based on Residual Estimation or Gradient Recovery
In this paper, we first derive a posteriori error estimators of residual type for the finite element approximation of the p-Laplacian, and show that they are reliable, and efficient up to higher order terms. We then construct some a posteriori error estimators based on gradient recovery. We further compare the two types of a posteriori error estimators. It is found that there exist some relationships between the two types of estimators, which are similar to those held in the case of the Laplacian. It is shown that the a posteriori error estimators based on gradient recovery are equivalent to the discretization error in a quasi-norm provided the solution is sufficiently smooth and mesh is uniform. Under stronger conditions, superconvergnece properties have been established for the used gradient recovery operator, and then some of the gradient recovery based estimates are further shown to be asymptotically exact to the discretization error in a quasi-norm. Numerical results demonstrating these a posteriori estimates are also presented. 相似文献
20.
Simon Shaw J. R. Whiteman 《Computer Methods in Applied Mechanics and Engineering》1997,150(1-4):397-409
This article contains a concise survey of the numerical analysis of Volterra equations, and leads up to some recent results on a posteriori error estimation for finite element approximations. 相似文献