High-order numerical method for 2D biharmonic interface problem

We present a robust and effective method for the numerical solution of the biharmonic interface problem with discontinuities in both the solution and its derivatives. We use a mixed scheme, in which the biharmonic equation is decoupled to two Poisson equations. The proposed approach is based on the method of difference potentials combined with finite difference schemes on regular structured grid to solve this problem with high-order accuracy on nonconforming domains. Representative numerical experiments confirm the accuracy and effectiveness of the proposed method and its ability to handle problems with coupled equations.