A posteriori error estimation and adaptive strategy for the control of MsFEM computations

被引：13

作者：

Chamoin, Ludovic ^{[1
,2
]}

Legoll, Frederic ^{[2
,3
]}

机构：

[1] Univ Paris Saclay, CNRS, ENS Cachan, LMT, 61 Ave President Wilson, F-94235 Cachan, France

[2] Inria Paris, MATHERIALS Project Team, 2 Rue Simone Iff,CS 42112, F-75589 Paris 12, France

[3] Paris Est Univ, ENPC, Lab Navier, 6 & 8 Ave Blaise Pascal, F-77455 Marne La Vallee 2, France

来源：

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING | 2018年 / 336卷

关键词：

Multiscale problems; MsFEM approach; A posteriori error estimation; Adaptivity; FINITE-ELEMENT-METHOD; ELLIPTIC PROBLEMS; MULTISCALE METHODS; BOUNDS; HOMOGENIZATION; APPROXIMATIONS; CONVERGENCE; GUARANTEED;

D O I：

10.1016/j.cma.2018.02.016

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

We introduce quantitative and robust tools to control the numerical accuracy in simulations performed using the Multiscale Finite Element Method (MsFEM). First, we propose a guaranteed and fully computable a posteriori error estimate for the global error measured in the energy norm. It is based on dual analysis and the Constitutive Relation Error (CRE) concept, with recovery of equilibrated fluxes from the approximate MsFEM solution. Second, the estimate is split into several indicators, associated to the various MsFEM error sources, in order to drive an adaptive procedure. The overall strategy thus enables to automatically identify an appropriate trade-off between accuracy and computational cost in the MsFEM numerical simulations. Furthermore, the strategy is compatible with the offline/online paradigm of MsFEM. The performances of our approach are demonstrated in several numerical experiments. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：1 / 38

页数：38

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