Online Mixed Multiscale Finite Element Method with Oversampling and Its Applications

被引：0
作者：
Yanfang Yang
Shubin Fu
Eric T. Chung
机构：
[1] Guangzhou University,School of Mathematics and Information Science
[2] The Chinese University of Hong Kong,Department of Mathematics
来源：
Journal of Scientific Computing | 2020年 / 82卷
关键词：
Multiscale; Mixed finite element; Oversampling; Heterogeneous media;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we consider an online basis enrichment mixed generalized multiscale method with oversampling, for solving flow problems in highly heterogeneous porous media. This is an extension of the online mixed generalized multiscale method (Chan et al. in Numer Math Theory Methods Appl 9(4):497–527, 2016). The multiscale online basis functions are computed by solving a Neumann problem in an over-sampled domain, instead of a standard neighborhood of a coarse face. We are motivated by the restricted domain decomposition method. Extensive numerical experiments are presented to demonstrate the performance of our methods for both steady-state flow, and two-phase flow and transport problems.
引用
收藏
相关论文
共 55 条
  • [1] Aarnes JE(2004)On the use of a mixed multiscale finite element method for greater flexibility and increased speed or improved accuracy in reservoir simulation Multiscale Model. Simul. 2 421-439
  • [2] Aarnes JE(2005)Mixed multiscale finite elements and streamline methods for reservoir simulation of large geomodels Adv. Water Resour. 28 257-271
  • [3] Kippe V(2004)Analysis of a two-scale, locally conservative subgrid upscaling for elliptic problems SIAM J. Numer. Anal. 42 576-598
  • [4] Lie K-A(2007)A multiscale mortar mixed finite element method Multiscale Model. Simul. 6 319-346
  • [5] Arbogast T(1999)A restricted additive Schwarz preconditioner for general sparse linear systems SIAM J. Sci. Comput. 21 792-797
  • [6] Arbogast T(2016)Adaptive mixed GMsFEM for flows in heterogeneous media. Numer. Math. Theory Methods Appl. 9 497-527
  • [7] Pencheva G(2002)A mixed multiscale finite element method for elliptic problems with oscillating coefficients Math. Comput. 72 541-576
  • [8] Wheeler MF(2015)Mixed generalized multiscale finite element methods and applications. Multiscale Model. Simul. 13 338-366
  • [9] Yotov I(2015)Residual-driven online generalized multiscale finite element methods. J. Comput. Phys. 302 176-190
  • [10] Cai X-C(2017)An online generalized multiscale discontinuous galerkin method (GMsDGM) for flows in heterogeneous media Commun. Comput. Phys. 21 401-422
123456