SC 98-10 Ralf Kornhuber: Monotone Iterations for Elliptic Variational Inequalities Appeared in: I. Athanasopoulos, G. Makrakis, J. Rodriques
(eds.) Free Boundary Problems, Theory and Applications
Abstract: A wide range of free boundary problems occurring in
engineering andindustry can be rewritten as a minimization problem
for astrictly convex, piecewise smooth but non-differentiable energy
functional.The fast solution of related discretized problemsis a very
delicate question, because usual Newton techniquescannot be
applied.
We propose a new approach based
on convex minimization
and constrained Newton type linearization.
While convex minimization provides global
convergence of the overall
iteration, the subsequent constrained
Newton type linearization is intended to
accelerate the convergence speed.
We present a general convergence
theory and discuss several applications.
Keywords: finite elements,
multigrid methods,
variational inequalities
MSC: 65N55, 65K10, 49M20, 49M15