Table of Contents
International Journal of Partial Differential Equations
Volume 2013 (2013), Article ID 476873, 13 pages
http://dx.doi.org/10.1155/2013/476873
Research Article

A Numerical Method for Solving 3D Elasticity Equations with Sharp-Edged Interfaces

1Department of Mathematics, College of Science, China University of Petroleum, Beijing 102249, China
2Department of Mathematics and Statistics, Louisiana Tech University, Ruston, LA 71272, USA

Received 11 April 2013; Revised 16 June 2013; Accepted 25 June 2013

Academic Editor: Yuri N. Skiba

Copyright © 2013 Liqun Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Interface problems occur frequently when two or more materials meet. Solving elasticity equations with sharp-edged interfaces in three dimensions is a very complicated and challenging problem for most existing methods. There are several difficulties: the coupled elliptic system, the matrix coefficients, the sharp-edged interface, and three dimensions. An accurate and efficient method is desired. In this paper, an efficient nontraditional finite element method with nonbody-fitting grids is proposed to solve elasticity equations with sharp-edged interfaces in three dimensions. The main idea is to choose the test function basis to be the standard finite element basis independent of the interface and to choose the solution basis to be piecewise linear satisfying the jump conditions across the interface. The resulting linear system of equations is shown to be positive definite under certain assumptions. Numerical experiments show that this method is second order accurate in the norm for piecewise smooth solutions. More than 1.5th order accuracy is observed for solution with singularity (second derivative blows up).