An a posteriori error indicator for discontinuous Galerkin approximations of fourth-order elliptic problems

被引：51

作者：

Georgoulis, Emmanuil H. ^{[1
]}

Houston, Paul ^{[2
]}

Virtanen, Juha ^{[1
]}

机构：

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

[2] Univ Nottingham, Sch Math Sci, Nottingham NG7 2RD, England

来源：

IMA JOURNAL OF NUMERICAL ANALYSIS | 2011年 / 31卷 / 01期

关键词：

Discontinuous Galerkin methods; biharmonic problem; fourth order PDEs; a posteriori error analysis; adaptivity; FINITE-ELEMENT APPROXIMATIONS; FAMILY; PLATES;

D O I：

10.1093/imanum/drp023

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce a residual-based a posteriori error indicator for discontinuous Galerkin discretizations of the biharmonic equation with essential boundary conditions. We show that the indicator is both reliable and efficient with respect to the approximation error measured in terms of a natural energy norm under minimal regularity assumptions. We validate the performance of the indicator within an adaptive mesh refinement procedure and show its asymptotic exactness for a range of test problems.

引用

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页码：281 / 298

页数：18

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