Averaging techniques for reliable a posteriori FE-error control in elastoplasticity with hardening

被引：20
作者：
Carstensen, C
Alberty, J
机构：
[1] Vienna Univ Technol, Inst Appl Math & Numer Anal, A-1040 Vienna, Austria
[2] Univ Kiel, Math Seminar, D-24098 Kiel, Germany
来源：
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING | 2003年 / 192卷 / 11-12期
关键词：
elastoplasticity; variational inequality; a posteriori error estimate; plasticity with hardening; viscoplasticity; primal problem; dual problem; reliability; finite element method; averaging estimator;
D O I：
10.1016/S0045-7825(02)00648-5
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
Averaging techniques are popular tools in adaptive finite element methods for numerical simulation in continuum mechanics since they provide efficient a posteriori error control. In this paper, the reliability of any averaging estimator is shown for low order finite element methods in one time-step of elastoplasticity with hardening. The constants and higher-order terms are effected by the hardening and the smoothness of given right-hand sides, but are independent of the structure of a shape-regular mesh. Since it involves a different functional analytical framework, the case of perfect plasticity is excluded from this paper. (C) 2002 Elsevier Science B.V. All rights reserved.
引用
收藏
页码：1435 / 1450
页数：16
相关论文
共 33 条
[1]   Adaptive numerical analysis in primal elastoplasticity with hardening [J].
Alberty, J ;
Carstensen, C ;
Zarrabi, D .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1999, 171 (3-4) :175-204
[2]   Numerical analysis of time-depending primal elastoplasticity with hardening [J].
Alberty, J ;
Carstensen, C .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2000, 37 (04) :1271-1294
[3]  
ALBERTY J, 2000, THESIS U KIEL
[4]  
BARTELS S, 2000, BERICHTSREIHE MATH S
[5]   Edge residuals dominate A posteriori error estimates for low order finite element methods [J].
Carsten, C ;
Verfürth, R .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1999, 36 (05) :1571-1587
[6]   Coupling of FEM and BEM for interface problems in viscoplasticity and plasticity with hardening [J].
Carstensen, C .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1996, 33 (01) :171-207
[7]   Numerical analysis of the primal problem of elastoplasticity with hardening [J].
Carstensen, C .
NUMERISCHE MATHEMATIK, 1999, 82 (04) :577-597
[8]   Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. Part I: Low order conforming, nonconforming, and mixed FEM [J].
Carstensen, C ;
Bartels, S .
MATHEMATICS OF COMPUTATION, 2002, 71 (239) :945-969
[9]  
Carstensen C, 1999, RAIRO-MATH MODEL NUM, V33, P1187
[10]   Averaging technique for FE -: a posteriori error control in elasticity.: Part II:: λ-independent estimates [J].
Carstensen, C ;
Funken, SA .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2001, 190 (35-36) :4663-4675
1234