The singular finite element method for some elliptic boundary value problem with interface

Authors:
Jicheng Jin;Xiaonan Wu
Affiliations:
Department of Mathematics, Xiangtan University, Xiangtan, Hunan province, China;Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong
Venue:
Journal of Computational and Applied Mathematics
Year:
2004

Citing 3
Cited 0

A finite element method for large domains

Computer Methods in Applied Mechanics and Engineering
The p-version of the finite element method for the elliptic boundary value problems with interfaces

Computer Methods in Applied Mechanics and Engineering
A Finite-Element Method for Laplace- and Helmholtz-Type Boundary Value Problems with Singularities

SIAM Journal on Numerical Analysis

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Abstract

A kind of numerical method is proposed for some elliptic boundary value problems with interface. It includes mainly two steps. At the first step, we obtain the approximation of the singularity near the singular points by solving a simple eigenvalue problem, which is one dimension less than the original problem. At the second step, we apply the approximation of the singularity together with the standard finite element basis functions to construct the singular finite element space and finally solve the original problem on a conventional mesh. Some numerical examples show the effectiveness of this method.