A discontinuous Galerkin finite element method for swelling model of polymer gels

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:398

Article

Li, Huanrong^2,3  Li, Yukun¹ 

[1] Univ Tennessee, Dept Math, Knoxville, TN 37996 USA

[2] Chongqing Univ Technol & Business, Coll Math & Stat, Chongqing 400067, Peoples R China

[3] Chinese Acad Sci, Inst Atmospher Phys, LASG, Beijing 100029, Peoples R China

关键词: Gel model;    Soft matters;    Discontinuous Galerkin method;    Error estimates;    Numerical examples;   

DOI  :  10.1016/j.jmaa.2012.08.033

来源: Elsevier

【 摘 要 】

An attractive feature of discontinuous Galerkin (DG) finite element schemes is that this concept offers a unified and versatile discretization platform for various types of partial differential equations. The locality of the trial functions not only supports local mesh refinements but also offers a framework for comfortably varying the order of the discretization. In this paper, we propose and analyze a mixed-DG finite element method for a displacement-pressure model which describes swelling dynamics of polymer gels under mechanical constraints. By introducing a flux variable we first present a reformulation of the governing equations of polymer gels. We then approximate the pressure and flux variables by a mixed finite element space and the displacement by DG finite element method. Existence and uniqueness are proved and error estimates are derived for mixed-DG finite element scheme. Finally, numerical experiments are presented to show the performance of the mixed-DG approximation of polymer gels. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

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