Advanced Numerical Methods in the Mathematical Sciences

• May 4–7, 2015
• Texas A&M University
• College Station, TX
• Rudder Tower (RDER) 501

Johnny Guzmán, Brown University

Higher-Order Finite Element Methods for Elliptic Problems with Interface

Authors

• Johnny Guzmán
• Manuel Sanchez-Uribe
• Marcus Sarkis

Abstract

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.