ERROR REDUCTION,CONVERGENCE AND OPTIMALITY OF AN ADAPTIVE MIXED FINITE ELEMENT METHOD

This paper proves the error reduction property(saturation property),convergence and optimality of an adaptive mixed finite element method(AMFEM) for the Poisson equation.In each step of AMFEM,the local refinement is performed basing on simple either edge-oriented residuals or edge-oriented data oscillations,depending only on the marking strategy,under some restriction of refinement.The main tools used here are the strict discrete local efficiency property given by Carstensen and Hoppe(2006) and the quasi-orthogonality estimate proved by Chen,Hoist,and Xu (2009).Numerical experiments fully confirm the theoretical analysis.