Preprint No. A-01-10

Ralf Kornhuber

Nonlinear multigrid techniques

Abstract: In these introductory notes, we focus on smooth and piecewise smooth semilinear elliptic partial differential equations in the framework of convex minimization problems. We present and analyze old and new nonlinear multigrid techniques. Related procedures are often used without proof in practical applications. After a brief motivation of linear multigrid, we principally concentrate on Newton multigrid for smooth problems and on monotone multigrid for the piecewise smooth case.

Keywords: nonlinear pdes, variational inequalities, finite elements, Newton method, multigrid methods

Mathematics Subject Classification (MSC2000): 65N22, 65N30, 65N55, 65K10

Language: ENG

Available: Pr-A-01-10.ps Pr-A-01-10.ps.gz

Contact: Ralf Kornhuber, Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, D-14195 Berlin, Germany (kornhube@math.fu-berlin.de)

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