Goal-oriented adaptivity for GMsFEM

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:296

Article

Chung, Eric T.¹  Leung, Wing Tat²  Pollock, Sara² 

[1] Chinese Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China

[2] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

关键词: High-contrast flow;    Multiscale finite element methods;    A posteriori error estimation;    Goal-oriented adaptivity;    Adaptive enrichment;   

DOI  :  10.1016/j.cam.2015.10.021

来源: Elsevier

【 摘 要 】

In this paper we develop two goal-oriented adaptive strategies for a posteriori error estimation within the generalized multiscale finite element framework. In this methodology, one seeks to determine the number of multiscale basis functions adaptively for each coarse region to efficiently reduce the error in the goal functional. Our first error estimator uses a residual based strategy where local indicators on each coarse neighborhood are the product of local indicators for the primal and dual problems, respectively. In the second approach, viewed as the rnultiscale extension of the dual weighted residual method (DWR), the error indicators are computed as the pairing of the local H-1 residual of the primal problem weighed by a projection into the primal space of the H-0(1) dual solution from an enriched space, over each coarse neighborhood. In both of these strategies, the goal-oriented indicators are then used in place of a standard residual-based indicator to mark coarse neighborhoods of the mesh for further enrichment in the form of additional multiscale basis functions. The method is demonstrated on high-contrast problems with heterogeneous multiscale coefficients, and is seen to outperform the standard residual based strategy with respect to efficient reduction of error in the goal function. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

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