A posteriori error estimation for the finite element method-of-lines solution of parabolic problems

被引：32

作者：

Adjerid, S ^{[1
]}

Flaherty, JE

Babuska, I

机构：

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

[2] Rensselaer Polytech Inst, Dept Comp Sci, Troy, NY 12180 USA

[3] Rensselaer Polytech Inst, Sci Computat Res Ctr, Troy, NY 12180 USA

[4] Univ Texas, Texas Inst Computat & Appl Math, Austin, TX 78712 USA

来源：

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | 1999年 / 9卷 / 02期

关键词：

D O I：

10.1142/S0218202599000142

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Babuska and Yu constructed a posteriori estimates for finite element discretization errors of linear elliptic problems utilizing a dichotomy principal stating that the errors of odd-order approximations arise near element edges as mesh spacing decreases while those of even-order approximations arise in element interiors. We construct similar a posteriori estimates for the spatial errors of finite element method-of-lines solutions of linear parabolic partial differential equations on square-element meshes. Error estimates computed in this manner are proven to be asymptotically correct; thus, they converge in strain energy under mesh refinement at the same rate as the actual errors.

引用

页码：261 / 286

页数：26

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