Commun. Comput. Phys., 12 (2012), pp. 595-612. A Numerical Method for Solving Elasticity Equations with Interfaces Songming Hou 1*, Zhilin Li 2, Liqun Wang 1, Wei Wang 11 Department of Mathematics and Statistics, Louisiana Tech University, Ruston, LA, 71272, USA. 2 Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA; and Nanjing Normal University, China. Received 16 September 2010; Accepted (in revised version) 13 July 2011 Available online 20 February 2012 doi:10.4208/cicp.160910.130711s 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 $L^{\infty}$ 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. AMS subject classifications: 65N30 Notice: Undefined variable: pac in /var/www/html/issue/abstract/readabs.php on line 164 Key words: Elasticity equations, non-body fitted mesh, finite element method, jump condition. *Corresponding author. Email: shou@latech.edu (S. Hou), zhilin@math.ncsu.edu (Z. Li), wliqunhmily@gmail.com (L. Wang), htprww@gmail.com (W. Wang)