A Posteriori Error Bounds for Discontinuous Galerkin Methods for Quasilinear Parabolic Problems

被引：3

作者：

Georgoulis, Emmanuil H. ^{[1
]}

Lakkis, Omar ^{[2
]}

机构：

[1] Univ Leicester, Dept Math, Univ Rd, Leicester LE1 7RH, Leics, England

[2] Univ Sussex, Dept Math, Falmer BN1 9RF, E Sussex, England

来源：

NUMERICAL MATHEMATICS AND ADVANCED APPLICATIONS 2009 | 2010年

关键词：

2ND-ORDER ELLIPTIC PROBLEMS; FINITE-ELEMENT METHODS; DIFFUSION EQUATIONS; APPROXIMATIONS; RECONSTRUCTION;

D O I：

10.1007/978-3-642-11795-4_37

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We derive a posteriori error bounds for a quasilinear parabolic problem, which is approximated by the hp-version interior penalty discontinuous Galerkin method (IPDG). The error is measured in the energy norm. The theory is developed for the semidiscrete case for simplicity, allowing to focus on the challenges of a posteriori error control of IPDG space-discretizations of strictly monotone quasilinear parabolic problems. The a posteriori bounds are derived using the elliptic reconstruction framework, utilizing available a posteriori error bounds for the corresponding steady-state elliptic problem.

引用

页码：351 / 358

页数：8

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