Dual formulations of mixed finite element methods with applications

被引：24

作者：

Gillette, Andrew ^{[1
]}

Bajaj, Chandrajit ^{[2
]}

机构：

[1] Univ Texas Austin, Dept Math, Austin, TX 78712 USA

[2] Univ Texas Austin, Dept Comp Sci, Austin, TX 78712 USA

来源：

COMPUTER-AIDED DESIGN | 2011年 / 43卷 / 10期

关键词：

Discrete exterior calculus; Finite element method; Partial differential equations; Whitney forms; Hodge star; HODGE THEORY; CONSTRUCTION;

D O I：

10.1016/j.cad.2011.06.017

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

Mixed finite element methods solve a PDE using two or more variables. The theory of Discrete Exterior Calculus explains why the degrees of freedom associated to the different variables should be stored on both primal and dual domain meshes with a discrete Hodge star used to transfer information between the meshes. We show through analysis and examples that the choice of discrete Hodge star is essential to the numerical stability of the method. Additionally, we define interpolation functions and discrete Hodge stars on dual meshes which can be used to create previously unconsidered mixed methods. Examples from magnetostatics and Darcy flow are examined in detail. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：1213 / 1221

页数：9

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