Convergence and Quasi-Optimality of an Adaptive Continuous Interior Penalty Finite Element Method

Abstract

An adaptive continuous interior penalty finite element method (ACIPFEM) for symmetric second order linear elliptic equations is considered. Convergence and quasi-optimality of the ACIPFEM are proved. Compared with the analyses for the adaptive finite element method or the adaptive interior penalty discontinuous Galerkin method, extra work is done to overcome the difficulties caused by the additional penalty term. Numerical tests are provided to verify the theoretical results and show advantages of the ACIPFEM.