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A note on the approximation of free boundaries by finite element methods. (English) Zbl 0596.65092
The aim of the present paper is to study rates of convergence in measure (and in distance) for the approximate free boundaries (they are defined as suitable level set). The results are applied to the primal and mixed formulation of the obstacle problem and to singular parabolic problems (the two-phase Stefan problem and the porous medium equation) in several variables.
Main result: If an \(L^ p\)-error estimate is known with \(p<\infty\), then the rates of convergence for the free boundaries are in measure, error estimates in distance are obtained for \(p=\infty\).
Reviewer: J.Lovíšek

65Z05 Applications to the sciences
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35K05 Heat equation
80A17 Thermodynamics of continua
35R35 Free boundary problems for PDEs
76S05 Flows in porous media; filtration; seepage
Full Text: DOI EuDML
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