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

页码：1435 / 1450

页数：16

共 13 条

[1] Reliable and efficient equilibrated a posteriori finite element error control in elastoplasticity and elastoviscoplasticity with hardening
Carstensen, C
Klose, R
Orlando, A
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2006, 195 (19-22) : 2574 - 2598
[2] Averaging techniques yield reliable a posteriori finite element error control for obstacle problems
S. Bartels
C. Carstensen
Numerische Mathematik, 2004, 99 : 225 - 249
[3] Reliable and efficient averaging techniques as universal tool for a posteriori finite element error control on unstructured grids
Carstensen, Carsten
INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2006, 3 (03) : 333 - 347
[4] All first-order averaging techniques for a posteriori finite element error control on unstructured grids are efficient and reliable
Carstensen, C
MATHEMATICS OF COMPUTATION, 2004, 73 (247) : 1153 - 1165
[5] Averaging technique for FE -: a posteriori error control in elasticity.: Part II:: λ-independent estimates
Carstensen, C
Funken, SA
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2001, 190 (35-36) : 4663 - 4675
[6] Averaging technique for FE - a posteriori error control in elasticity. Part I: Conforming FEM
Carstensen, C
Funken, SA
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2001, 190 (18-19) : 2483 - 2498
[7] Averaging techniques for the a posteriori bem error control for a hypersingular integral equation in two dimensions
Carstensen, Carsten
Praetorius, Dirk
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2007, 29 (02) : 782 - 810
[8] Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. Part II: Higher order FEM
Bartels, S
Carstensen, C
MATHEMATICS OF COMPUTATION, 2002, 71 (239) : 971 - 994
[9] Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. Part I: Low order conforming, nonconforming, and mixed FEM
Carstensen, C
Bartels, S
MATHEMATICS OF COMPUTATION, 2002, 71 (239) : 945 - 969
[10] Averaging technique for a posteriori error control in elasticity. Part III: Locking-free nonconforming FEM
Carstensen, C
Funken, SA
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2001, 191 (8-10) : 861 - 877

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