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Finite element methods for parabolic free boundary problems. (English) Zbl 0733.65089
Advances in numerical analysis. Vol. I: Nonlinear partial differential equations and dynamical systems, Proc. 4th Summer Sch., Lancaster/UK 1990, 34-95 (1991).
[For the entire collection see Zbl 0724.00022.]
The author summarizes in detail previous work on finite element methods for parabolic free boundary problems. After discussing regularization and phase relaxation, the discretization is described, which is then followed by a stability analysis. Error analysis and mesh adaption form the contents of the following chapters. Finally, some exercises and numerical experiments are presented. The paper is strongly recommended for an analysis of the Stefan problem.
Reviewer: E.Krause (Aachen)

MSC:
65Z05 Applications to the sciences
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35K15 Initial value problems for second-order parabolic equations
35R35 Free boundary problems for PDEs
80A22 Stefan problems, phase changes, etc.
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs