A generalized finite difference method for solving elasticity interface problems

Abstract

In this paper, a generalized finite difference method (GFDM) is proposed to solve the elasticity interface problem. This method turns the original elasticity interface problem to be some coupled non-interface subproblems. A large sparse matrix can be yielded by those subproblems. Since this method makes the interface become a part of boundaries of subproblems, it can deal well with problems with complex geometrical interfaces. Moreover, this method can also deal well with the interface conditions with derivatives, because the GFDM uses a linear summation of nearby nodal values to express the derivatives of unknown variables. Numerical examples are provided to verify the accuracy and stability of the proposed method for elasticity interface problems. They show that the H-1 error of the method has the almost same convergence rate as the L-2 error and the size of jumps in the interface conditions only has a little effect on the stability of the proposed method.