Explicit a posteriori Local Error Estimation for Finite Element Solutions

Abstract

Abstract. For the finite element solution of Poisson’s equation, a local a posteriori error estimation based on the Hypercircle method is proposed. Even for the solution of Poisson’s equation without the H² regularity, this method can provide explicit local error estimation. The efficiency of the proposed method is demonstrated by numerical experiments for the boundary value problem of Poisson’s equation defined on the 2D and 3D domains.