An alternating direction Galerkin method for elliptic problems with gradient nonlinearity

Abstract

AbstractSeveral problems in many applications involve the solution of partial differential equations with gradient dependent nonlinearity. The numerical solution of the resulting nonlinear system is rather expensive. We present an alternating direction Galerkin method that allows much faster solution of the nonlinear system. The alternating direction formulation help reduce the problem into a sequence of nonlinear systems that may be solved very efficiently. Theoretical study of the convergence of the method will also be presented. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)