Convergence of adaptive mixed finite element method for convection-diffusion-reaction equations

摘要

We prove the convergence of an adaptive mixed finite element method (AMFEM)for (nonsymmetric) convection-diffusion-reaction equations. The convergenceresult holds from the cases where convection or reaction is not present toconvection-or reaction-dominated problems. A novel technique of analysis isdeveloped without any quasi orthogonality for stress and displacementvariables, and without marking the oscillation dependent on discrete solutionsand data. We show that AMFEM is a contraction of the error of the stress anddisplacement variables plus some quantity. Numerical experiments confirm thetheoretical results.