Report Number: CS-TR-78-674
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.