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A Numerical Method for Solving Elasticity Equations with Interfaces

Published online by Cambridge University Press:  20 August 2015

Songming Hou ,
Zhilin Li ,
Liqun Wang  and
Wei Wang
Songming Hou*
Affiliation:
Department of Mathematics and Statistics, Louisiana Tech University, Ruston, LA, 71272, USA
Zhilin Li*
Affiliation:
Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA; and Nanjing Normal University, China
Liqun Wang*
Affiliation:
Department of Mathematics and Statistics, Louisiana Tech University, Ruston, LA, 71272, USA
Wei Wang*
Affiliation:
Department of Mathematics and Statistics, Louisiana Tech University, Ruston, LA, 71272, USA
*
Corresponding author.Email:shou@latech.edu
Email:zhilin@math.ncsu.edu
Email:wliqunhmily@gmail.com
Email:htprww@gmail.com
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Abstract

Solving elasticity equations with interfaces is a challenging problem for most existing methods. Nonetheless, it has wide applications in engineering and science. An accurate and efficient method is desired. In this paper, an efficient non-traditional finite element method with non-body-fitting grids is proposed to solve elasticity equations with interfaces. 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 L∞ norm for piecewise smooth solutions. More than 1.5th order accuracy is observed for solution with singularity (second derivative blows up) on the sharp-edged interface corner.

Keywords

65N30Elasticity equationsnon-body fitted meshfinite element methodjump condition
Type
Research Article
Information
Communications in Computational Physics , Volume 12 , Issue 2 , August 2012 , pp. 595 - 612
Copyright
Copyright © Global Science Press Limited 2012

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