Monotone Iterations for Elliptic Variational Inequalities

Please always quote using this URN: urn:nbn:de:0297-zib-3539

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.

Metadaten
Author:	Ralf Kornhuber
Document Type:	ZIB-Report
Tag:	finite elements; multigrid methods; variational inequalities
MSC-Classification:	49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Mxx Numerical methods [See also 90Cxx, 65Kxx] / 49M15 Newton-type methods
	49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Mxx Numerical methods [See also 90Cxx, 65Kxx] / 49M20 Methods of relaxation type
	65-XX NUMERICAL ANALYSIS / 65Kxx Mathematical programming, optimization and variational techniques / 65K10 Optimization and variational techniques [See also 49Mxx, 93B40]
	65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N55 Multigrid methods; domain decomposition
Date of first Publication:	1998/03/12
Series (Serial Number):	ZIB-Report (SC-98-10)
ZIB-Reportnumber:	SC-98-10
Published in:	Appeared in: I. Athanasopoulos, G. Makrakis, J. Rodriques (eds.) Free Boundary Problems, Theory and Applications

Open Access