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An efficient linear scheme to approximate parabolic free boundary problems: Error estimates and implementation. (English) Zbl 0657.65131

A multidimensional nonlinear parabolic problem (which includes the two- phase Stefan problem and the porous medium equation) is considered from both a theoretical and a computational viewpoint.
“The numerical algorithm consists of approximating at each time step a linear elliptic partial differential equation by piecewise linear finite elements and then making an element - by - element algebraic correction to account for the nonlinearity”. The stability of the discrete scheme in energy and maximum norms is proved. Several energy error estimates for physical unknowns are derived, too. The implementation of the method (efficient solvers for linear systems involved) and some numerical experiments are discussed in the last section.
Reviewer: C.-I.Gheorghiu

MSC:

65Z05 Applications to the sciences
65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
76S05 Flows in porous media; filtration; seepage
35R35 Free boundary problems for PDEs
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