Overlapping Schwarz algorithms for nonlinear elliptic finite element problems

Xiao-Chuan Cai

Department of Mathematics, University of Kentucky, Lexington, KY 40506-0027


We consider the solution of systems of nonlinear algebraic equations that arise from the finite element discretization of nonlinear elliptic equations. The class of overlapping Schwarz algorithms has been extensively studied for linear problems. In this presentation, we extend the applicability of the algorithms to nonlinear elliptic problems. A combined overlapping additive Schwarz and inexact Newton algorithm will be discussed. Numerical results for two dimensional problems will also be reported.