Stopping criteria for nonlinear variational problems: iterative approach

Abstract In this paper, we present and study a stopping criteria based on a priori error estimate for nonlinear variational problems. We show that for nonlinear variational problems, the a priori error estimate is divided into two sub errors namely: the discretization error and the linearization error. We then used that representation to devise a stopping criteria that help to reduce the computational time. The methodology is applied to three problems and the numerical results demonstrate the superiority of the new approach.