Error Reduction And Convergence For An Adaptive Mixed Finite Element Method

Abstract

An adaptive mixed finite element method (AMFEM) is designed to guarantee an error reduction, also known as saturation property: After each refinement step, the error for the fine mesh is strictly smaller than the error for the coarse mesh up to oscillation terms. This error reduction property is established here for the Raviart-Thomas finite element method with a reduction factor $ \rh