Adaptive FAS-multigrid method for nonlinear elliptic equations on unstructured grids

Abstract

A two-step, node-wise assembly procedure is developed to enhance the classical assembly process that is repeatedly required for the nonlinear finite elements method. Using the proposed assembly method, an efficient nonlinear point-wise Gauss–Seidel method is designed and used as a smoother in a full approximation storage multigrid (FAS_MG) that results in solving nonlinear problems on unstructured grids as efficient as the linear ones. Next, the FAS_MG solver is incorporated into an adaptive full multigrid cycle that solves the nonlinear problem on a coarse grid and uses a posteriori error estimator to adaptively and automatically construct a next finer grid. Numerical results show that the proposed method solves adaptively nonlinear finite elements elliptic problems within the textbook MG efficiency. Copyright © 2007 John Wiley & Sons, Ltd.