A penalty/Newton/conjugate gradient method for the solution of obstacle problems

Motivated by the search for non-negative solutions of a system of Eikonal equations with Dirichlet boundary conditions, we discuss in this Note a method for the numerical solution of parabolic variational inequality problems for convex sets such as K = {v\ v is an element of H-0(1)(Omega), v greater than or equal to psi a.e. on Omega}. The numerical methodology combines penalty and Newton's method, the linearized problems being solved by a conjugate gradient algorithm requiring at each iteration the solution of a linear problem for a discrete analogue of the elliptic operator 1 - muDelta. Numerical experiments show that the resulting method has good convergence properties, even for small values of the penalty parameter. (C) 2003 Academie des sciences/Editions scientifiques et medicales Elsevier SAS. All rights reserved.