Advanced Numerical Methods in the Mathematical Sciences
- Johnny Guzmán, Brown University
- Higher-Order Finite Element Methods for Elliptic Problems with Interface
- Johnny Guzmán
- Manuel Sanchez-Uribe
- Marcus Sarkis
We present higher-order piecewise continuous finite element methods for solving a class of interface problems in two dimensions. The method is based on correction terms added to the right-hand side in the standard variational formulation of the problem. We prove optimal error estimates of the methods on general quasi-uniform and shape regular meshes in maximum norms. In addition, we apply the method to a Stokes interface problem, adding correction terms for the velocity and the pressure, obtaining optimal convergence results.