WEAK RESIDUAL ERROR-ESTIMATES FOR SYMMETRICAL POSITIVE SYSTEMS

Abstract

A weak-residual type error estimation for finite element solutions of symmetric positive systems in the sense of Friedrichs' is proposed. The estimator calculates a residual error interior to an element with no consideration of boundary residual, thus allowing for element-by-element computations. The estimator is proved to be bounded by the exact error in suitably defined norm with multiple constants. A priori and a posteriori numerical estimates are presented for a forward-backward heat equation model problem.