2 p.m. - 3 p.m. Location: FN 2.102
Mathematics, Worcester Polytechnic Institute
Finite Elements Methods for Elliptic Problems with Interfaces
Interface problems arise in several applications including heart models, cochlea models, aquatic animal locomotion, blood cell motion, front-tracking in porous media flows and material science, to name a few. One of the difficulties in these problems is that solutions are normally not smooth across interfaces, and therefore standard numerical methods will lose accuracy near the interface unless the meshes align to it.
However, it is advantageous to have meshes that do not align with the interface, especially for time dependent problems where the interface moves with time. Remeshing at every time step can be prohibitively costly, can destroy the structure of the grid, can deteriorate the well-conditioning of the stiffness matrix, and affect the stability of the problem. In this talk we present higher-order piecewise continuous finite element methods for solving a class of interface problems where the finite element triangulation does not fit the interface. The method is based on correction terms added to the right-hand side of the discrete formulation of the problem. We prove optimal error estimates of the methods on general quasi-uniform and shape regular meshes in maximum norms. We discuss the method to Poisson and Stokes interface
problems, and about an extension of this technique to transmission problem
with high-contrast coefficients.
Sponsored by the Department of Mathematical Sciences