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A FD/FE method for anisotropic elliptic interface problems

WHEN: Tuesday, 2019, December 24-14:00

WHERE: Room 526, Xingjian Building

SPONSOR:School of Mathematical Science, Nanjing Normal University

SPEAKER(S):Zhilin Li



ABSTRACT: Anisotropic elliptic interface problems are important but hard to solve. There is limited literature on numerical methods based on structured meshes. Finite element methods are often preferred but the average error estimates cannot guarantee accuracy of the solution near or at the interface. Using a finite difference discretization, the coefficient matrix of the resulting linear system of equations is neither an SPD nor an M-matrix. In this work, we combine a finite element discretization at regular grid points whose coefficient part matrix is an SPD, while at irregular grid points, a finite difference discretization based on the maximum principle preserving method whose coefficient part matrix is an M-matrix. A multigrid method based a nine-point stencil is employed to solve the linear system of equations. A scaling strategy along the interface is proposed along with the discretization. Error analysis show that the global error is nearly second order accurate in the L-infinity norm except a fact of |log h|. Numerical examples including an application of flow past anisotropic materials will be presented.