Volume 12, Issue 2
A Numerical Method for Solving Elasticity Equations with Interfaces

Songming Hou, Zhilin Li, Liqun Wang & Wei Wang

Commun. Comput. Phys., 12 (2012), pp. 595-612.

Published online: 2012-12

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  • Abstract

Solvingelasticityequations withinterfacesisachallengingproblemformost 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 orderaccurateinthe L∞ norm for piecewise smooth solutions. More than 1.5th order accuracy is observed for solution with singularity (second derivativeblows up) onthe sharp-edgedinterfacecorner.

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COPYRIGHT: © Global Science Press

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