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A new numerical method for Stefan-type problems in a class of unsmooth functions. (English) Zbl 1207.35023

Summary: A new numerical method for obtaining the weak solution of the initial-boundary value problem for a nonlinear parabolic type equation in the domain with the free boundary is suggested. For this aim, a special auxiliary problem, which has some advantages over the main problem and is equivalent to the main problem in a definite sense, is introduced. Using the auxiliary problem, efficient and economical numerical algorithms from a computer point of view for obtaining the weak solution of the main problem are suggested. In addition, the auxiliary problem also permits us to determine the order of differentiability of the solution of the main problem.

MSC:

35A35 Theoretical approximation in context of PDEs
35K55 Nonlinear parabolic equations
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35R35 Free boundary problems for PDEs
35D30 Weak solutions to PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
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