Selfadaptive mesh modification for parabolic FBPs: Theory and computation. (English) Zbl 0716.65112

Nochetto, R. H.; Paolini, M.; Verdi, C.

Free boundary value problems, Proc. Conf., Oberwolfach/FRG 1989, Int. Ser. Numer. Math. 95, 181-206 (1990).

[For the entire collection see Zbl 0702.00021.]
As a further development of a previous paper of the authors [ISNM 88, 261-286 (1989; Zbl 0688.65071)] the two-phase Stefan problem formulated by the enthalpy method and discretized by finite differences in time and linear finite elements in the two space dimension is considered as a model example for the construction of a selfadaptive mesh modification algorithm. This algorithm automatically regenerates the mesh independence of the interface motion in order to equidistribute interpolation errors on the finite element triangulation.
The basic ideas of the method reflect the underlying degenerate parabolic structure. Beside a substantial discussion of the theoretical aspects the authors deal with the implementation. Especially, a modern data structure (Quadtree) which is based on a tree structure is applied to an efficient organization and modification of the nodes of the triangulation. Results on stability and error estimates are taken over from other papers of the authors. Finally, the results of numerical experiments are reported.

Reviewer: K.-H.Hoffmann

MSC:

65Z05	Applications to the sciences
65N50	Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35R35	Free boundary problems for PDEs
80A22	Stefan problems, phase changes, etc.
35K05	Heat equation

Keywords:

parabolic free boundary problems; two-phase Stefan problem; enthalpy method; finite differences in time; linear finite elements in the two space dimension; selfadaptive mesh modification algorithm; data structure; Quadtree; triangulation; stability; error estimates; numerical experiments

Citations:

Zbl 0702.00021; Zbl 0688.65071