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Dualität und Strafmethoden bei elliptischen Differentialgleichungen. (German) Zbl 0537.49019
A quite general theory for deriving convergence bounds in penalty methods is used to derive estimates in terms of the discretization and penalty parameters for linear and weakly nonlinear elliptic differential with Dirichlet boundary conditions. Two different possibilities for the choice of the penalty term are compared to each other with respect to the resulting convergence property.
Reviewer: A.Kirsch

49M30 Other numerical methods in calculus of variations (MSC2010)
35J65 Nonlinear boundary value problems for linear elliptic equations
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
49N15 Duality theory (optimization)
65N15 Error bounds for boundary value problems involving PDEs
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