Advances of finite element analysis for elliptic, parabolic and Maxwell interface equations

Abstract

The development of finite element methods for interface problems in the recent two decades is reviewed with an emphasis on elliptic, parabolic and Maxwell interface problems. We summarize some important results, e.g., regularity, variational forms, discretization schemes, numerical quadrature, interface approxima-fition, and convergence analysis. The state of the art for these problems is described along with the history of developments. Finally, we outline some applications governed by the PDE systems with interfaces.