Hermite finite elements for second order boundary value problems with sharp gradient discontinuities

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:246

Article

Ruas, Vitoriano^1,2 

[1] Univ Paris 06, CNRS, UMR 7190, Inst Jean Rond dAlembert, F-75252 Paris 05, France

[2] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Sao Carlos, SP, Brazil

关键词: Diffusion;    Finite elements;    Flow problems;    Hermite;    Parabolic equations;    Porous media;   

DOI  :  10.1016/j.cam.2012.08.027

来源: Elsevier

【 摘 要 】

In two recent papers the author introduced a finite element method to solve second order elliptic equations in N-dimensional space, for N = 2 and N = 3 respectively, providing flux continuity across inter-element boundaries on the basis of Hermite interpolation in an N-simplex. After defining this method in the framework of diffusion-like problems with anisotropic diffusion tensors, another N-simplex based Hermite finite element method to solve the same class of problems is considered. The latter can be viewed as a variant of the popular lowest-order Raviart-Thomas mixed element known as RT0. A convergence analysis of this method is given, showing that, in contrast to RT0, it is second order accurate in L-2. Some numerical examples comparing the three methods are given. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free