A residual-type a posteriori error estimate of finite volume element method for a quasi-linear elliptic problem

Abstract

Abstract. In this paper, we consider the a posteriori error estimates of the finite volume element method for the general second-order quasilinear elliptic problems over a convex polygonal domain in the plane, propose a residual-based error estimator and derive the global upper and local lower bounds on the approximation error in the H1-norm. Moreover, for some special quasilinear elliptic problems, we propose a residual-based a posteriori error estimator and derive the global upper bound on the error in the L2-norm. Numerical experiments are also provided to verify our theoretical results. Key words. quasilinear elliptic problem, finite volume element method, a posteriori error esti-mates. 1