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Energy error estimates for a linear scheme to approximate nonlinear parabolic problems. (English) Zbl 0635.65123
The authors estimate the rate of convergence of a semidiscretization scheme used in the nonlinear parabolic problem \(u_ t+Ab(u)=f(b(u))\) where A is a linear elliptic operator and b(s) \((s\in R^ 1)\) is a Lipschitz continuous nondecreasing function. The used approximation scheme is based on Chernoff’s formula, studied in the theory of nonlinear semigroups of contractions. On each time step it leads to the solution of a linear elliptic problem. The obtained energy type error estimates are discussed for both degenerate and non-degenerate equations. The obtained results can be applied to the Stefan problem and to the porous medium equations. A variational technique is used.
Reviewer: J.Kačur

MSC:
65N40 Method of lines for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
80A17 Thermodynamics of continua
76S05 Flows in porous media; filtration; seepage
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