A finite element method for elasticity interface problems with locally modified triangulations
H. Xie 1, Z. Li 2, Z. Qiao 31 Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455-0132, USA.
2 Center for Research in Scientific Computation and Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, USA.
3 Institute for Computational Mathematics and Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong.
Received by the editors March 30, 2009 and, in revised form, June 3, 2010.
A finite element method for elasticity systems with discontinuities in the coefficients and the flux across an arbitrary interface is proposed in this paper. The method is based on a Cartesian mesh with local modifications to the mesh. The total degrees of the freedom of the finite element method remains the same as that of the Cartesian mesh. The local modifications lead to a quasi-uniform body-fitted mesh from the original Cartesian mesh. The standard finite element theory and implementation are applicable. Numerical examples that involve discontinuous material coefficients and non-homogeneous jump in the flux across the interface demonstrate the efficiency of the proposed method.AMS subject classifications: 65N30
Key words: elasticity interface problem, body-fitted mesh, Cartesian mesh, discontinuous coefficient, locally modified triangulation, finite element method, jump conditions.
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