A priori and a posteriori error analyses of an augmented discontinuous Galerkin formulation

被引：6

作者：

Barrios, Tomas P. ^{[2
]}

Bustinza, Rommel ^{[1
]}

机构：

[1] Univ Concepcion, Dept Ingn Matemat, Concepcion, Chile

[2] Univ Catolica Santisima Concepcion, Dept Matemat & Fis Aplicadas, Concepcion, Chile

来源：

IMA JOURNAL OF NUMERICAL ANALYSIS | 2010年 / 30卷 / 04期

关键词：

discontinuous Galerkin; augmented formulation; a priori and a posteriori error estimates; FINITE-ELEMENT-METHOD; WAVELET-BASED STABILIZATION;

D O I：

10.1093/imanum/drn042

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We use Galerkin least squares terms to develop a more general stabilized discontinuous Galerkin method for elliptic problems in the plane with mixed boundary conditions. The unique solvability and optimal rate of convergence of this scheme, with respect to the h-version, are established. Furthermore, we include the corresponding a posteriori error analysis, which results in a reliable and efficient estimator. Finally, we present several numerical examples that show the capability of the adaptive algorithm to localize the singularities, confirming the theoretical properties of the a posteriori error estimate.

引用

页码：987 / 1008

页数：22

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