A Posteriori Error Estimates for Parabolic Variational Inequalities

被引：14

作者：

Achdou, Yves ^{[1
,2
]}

Hecht, Frederic ^{[2
]}

Pommier, David ^{[3
]}

机构：

[1] Univ Paris Diderot, UFR Math, F-75251 Paris 05, France

[2] Univ Paris 06, Lab Jacques Louis Lions, F-75252 Paris, France

[3] INRIA Rocquencourt, Projet MATHFI, F-78153 Le Chesnay, France

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2008年 / 37卷 / 03期

关键词：

Parabolic obstacle problems; Finite element methods; A posteriori error estimates; Adaptive mesh refinement;

D O I：

10.1007/s10915-008-9215-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study a posteriori error estimates in the energy norm for some parabolic obstacle problems discretized with a Euler implicit time scheme combined with a finite element spatial approximation. We discuss the reliability and efficiency of the error indicators, as well as their localization properties. Apart from the obstacle resolution, the error indicators vanish in the so-called full contact set. The case when the obstacle is piecewise affine is studied before the general case. Numerical examples are given.

引用

页码：336 / 366

页数：31

共 16 条

[1] Bergam A, 2005, MATH COMPUT, V74, P1117, DOI 10.1090/S0025-5718-04-01697-7
[2] Adaptive finite element methods with convergence rates
Binev, P
Dahmen, W
DeVore, R
[J]. NUMERISCHE MATHEMATIK, 2004, 97 (02) : 219 - 268
[3] Chen ZM, 2000, NUMER MATH, V84, P527, DOI 10.1007/s002119900123
[4] CIARLET P. G., 1978, The Finite Element Method for Elliptic Problems
[5] Ciarlet P.G., 1991, HDB NUMERICAL ANAL 1, P17, DOI DOI 10.1016/S1570-8659(05)80039-0
[6] ADAPTIVE FINITE-ELEMENT METHODS FOR PARABOLIC PROBLEMS .1. A LINEAR-MODEL PROBLEM
ERIKSSON, K
JOHNSON, C
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1991, 28 (01) : 43 - 77
[7] ADAPTIVE FINITE-ELEMENT METHODS FOR PARABOLIC PROBLEMS .2. OPTIMAL ERROR-ESTIMATES IN L-INFINITY-L(2) AND L-INFINITY-L-INFINITY
ERIKSSON, K
JOHNSON, C
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1995, 32 (03) : 706 - 740
[8] The primal-dual active set strategy as a semismooth Newton method
Hintermüller, M
Ito, K
Kunisch, K
[J]. SIAM JOURNAL ON OPTIMIZATION, 2003, 13 (03) : 865 - 888
[9] ADAPTIVE MULTILEVEL METHODS FOR OBSTACLE PROBLEMS
HOPPE, RHW
KORNHUBER, R
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1994, 31 (02) : 301 - 323
[10] Semi-smooth Newton methods for variational inequalities of the first kind
Ito, K
Kunisch, K
[J]. ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2003, 37 (01): : 41 - 62

← 1 2 →