Institution: Stanford University, Department of Computer Science

Title: Finite element approximation and iterative solution of a class of mildly non-linear elliptic equations

Author: Chan, Tony F.

Author: Glowinski, Roland

Date: November 1978

Abstract: We describe in this report the numerical analysis of a particular class of nonlinear Dirichlet problems. We consider an equivalent variational inequality formulation on which the problems of existence, uniqueness and approximation are easier to discuss. We prove in particular the convergence of an approximation by piecewise linear finite elements. Finally, we describe and compare several iterative methods for solving the approximate problems and particularly some new algorithms of augmented lagrangian type, which contain as special case some well-known alternating direction methods. Numerical results are presented.

http://i.stanford.edu/pub/cstr/reports/cs/tr/78/674/CS-TR-78-674.pdf