A POSTERIORI ENERGY-NORM ERROR ESTIMATES FOR ADVECTION-DIFFUSION EQUATIONS APPROXIMATED BY WEIGHTED INTERIOR PENALTY METHODS

• 来源期刊: 计算数学（英文版）
• 关键词: Discontinuous Galerkin Weighted interior penalty A posteriori error estimate Heterogeneous diffusion.Advection-diffusion
• 年，卷（期）: 2008,（4）
• 页码范围: 488-510
• 页数: 23页
• 语种: 英文

摘要

We propose and analyze a posteriori energy-norm error estimates for weighted interior penalty discontinuous Galerkin approximations of advection-diffusion-reaction equations with heterogeneous and anisotropic diffusion.The weights,which play a key role in the analysis.depend on the diffusion tensor and are used to formulate the consistency terms in the discontinuous Galerkin method.The error upper bounds,in which all the constants are specified.consist of three terms:a residual estimator which depends only on the elementwise fluctuation of the discrete solution residual,a diffusive flux estimator where the weights used in the method enter explicitly,and a non-conforming estimator which is nonzero because of the use of discontinuous finite element spaces.The three estimators can be bounded locally by the approximation error.A particular attention is given to the dependency on problem parameters of the constants in the local lower error bounds,For moderate advection.it.is shown that full robustness with respect to diffusion heterogeneities is achieved owing to the specific design of the weights in the discontinuous Galerkin method,while diffusion anisotropies remain purely local and impact the constants through the square root of the condition number of the diffusion tensor.For dominant advection,the local lower error bounds can be written with constants involving a cut-off for the ratio of local mesh size to the reciprocal of the square root of the lowest local eignevalue of the diffusion tensor.