The Discontinuous Galerkin Method for Two-dimensional Hyperbolic Problems Part II: A Posteriori Error Estimation

被引：38

作者：

Adjerid, Slimane ^{[1
]}

Baccouch, Mahboub ^{[1
]}

机构：

[1] Virginia Polytech Inst & State Univ, Dept Math, Blacksburg, VA 24061 USA

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2009年 / 38卷 / 01期

基金：

美国国家科学基金会;

关键词：

Discontinuous Galerkin method; Hyperbolic problems; Superconvergence; A posteriori error estimation; FINITE-ELEMENT METHODS; CONSERVATION-LAWS; SUPERCONVERGENCE; DIFFUSION;

D O I：

10.1007/s10915-008-9222-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this manuscript we construct simple, efficient and asymptotically correct a posteriori error estimates for discontinuous finite element solutions of scalar first-order hyperbolic partial differential problems on triangular meshes. We explicitly write the basis functions for the error spaces corresponding to several finite element spaces. The leading term of the discretization error on each triangle is estimated by solving a local problem. We also show global superconvergence for discontinuous solutions on triangular meshes. The a posteriori error estimates are tested on several linear and nonlinear problems to show their efficiency and accuracy under mesh refinement for smooth and discontinuous solutions.

引用

页码：15 / 49

页数：35

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