A Posteriori Error Estimates of Finite Volume Element Method for Second-Order Quasilinear Elliptic Problems

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 $H^1$-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 $L^2$-norm. Numerical experiments are also provided to verify our theoretical results.