A generalized multiscale finite element method for the Brinkman equation

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:280

Article

Galvis, Juan¹  Li, Guanglian^2,3  Shi, Ke^2,3 

[1] Univ Nacl Colombia, Dept Matemat, Bogota, DC, Colombia

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

[3] Texas A&M Univ, Inst Sci Computat, College Stn, TX 77843 USA

关键词: Brinkman equation;    Generalized multiscale finite element method;    Mixed finite element;   

DOI  :  10.1016/j.cam.2014.11.038

来源: Elsevier

【 摘 要 】

In this paper we consider the numerical upscaling of the Brinkman equation in the presence of high-contrast permeability fields. We develop and analyze a robust and efficient Generalized Multiscale Finite Element Method (GMsFEM) for the Brinkman model in two dimensions. In the fine grid, we use mixed finite element method with the velocity and pressure being continuous piecewise quadratic and piecewise constant finite element spaces, respectively. Using the GMsFEM framework we construct suitable coarse-scale spaces for the velocity and pressure that yield a robust mixed GMsFEM. We develop a novel approach to construct a coarse approximation for the velocity snapshot space and a robust small offline space for the velocity space. The stability of the mixed GMsFEM and a priori error estimates are derived. A variety of two-dimensional numerical examples are presented to illustrate the effectiveness of the algorithm. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free