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A generalized finite difference method for solving biharmonic interface problems
Engineering Analysis With Boundary Elements  (IF2.964),  Pub Date : 2021-11-29, DOI: 10.1016/j.enganabound.2021.11.001
Yanan Xing, Lina Song, Po-Wei Li

In this paper, a meshless discrete scheme based on the generalized finite difference method (GFDM) is proposed to solve the biharmonic interface problem. This scheme turns the interface problem to be two non-interface subproblems coupled with the interface conditions. The interface conditions act as the boundary conditions of the subproblems because the interface plays the role of their boundary. Therefore, the proposed method has the advantage of dealing with problems with complex geometrical interfaces. Due to the GFDM approximates the derivatives of the unknown variables by using a linear combination of the values for nearby nodes, the proposed method also has the advantage in dealing with the interface condition with the jump of derivatives. Four numerical examples are provided to verify the accuracy and the stability of the GFDM for biharmonic interface problems. The numerical results show that the H1 errors can reach almost the same convergence rate of the L and L2 errors. The convergence rates are almost and even higher than fourth-order when the fourth-order Taylor Series expansion is adopted in the GFDM.