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An Adaptive Multilevel Approach to Parabolic Equations III.

Please always quote using this URN: urn:nbn:de:0297-zib-519
  • Part III of the paper is devoted to the construction of an adaptive FEM solver in two spatial dimensions, which is able to handle the singularly perturbed elliptic problems arising from discretization in time. The problems of error estimation and multilevel iterative solution of the linear systems - both uniformly well behaved with respect to the time step - can be solved simultaneously within the framework of preconditioning. A multilevel nodal basis preconditioner able to handle highly nonuniform meshes is derived. As a numerical example an application of the method to the bioheat-transfer equation is included. {\bf AMS CLASSIFICATION:} 65F10, 65F35, 65M50, 65M60, 65N30.

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Metadaten
Author:Folkmar A. Bornemann
Document Type:ZIB-Report
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F10 Iterative methods for linear systems [See also 65N22]
65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F35 Matrix norms, conditioning, scaling [See also 15A12, 15A60]
65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M50 Mesh generation and refinement
65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Date of first Publication:1991/01/15
Series (Serial Number):ZIB-Report (SC-91-01)
ZIB-Reportnumber:SC-91-01
Published in:Appeared in: IMPACT Comput. Sci. Engrg. 4, (1992) pp. 1-45
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