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Concepts of an Adaptive Hierarchical Finite Element Code.

Please always quote using this URN: urn:nbn:de:0297-zib-131
  • The paper presents the mathematical concepts underlying the new adaptive finite element code KASKADE, which, in its present form, applies to linear scalar second-order 2-D elliptic problems on general domains. Starting point for the new development is the recent work on hierarchical finite element bases due to Yserentant (1986). It is shown that this approach permits a flexible balance between iterative solver, local error estimator, and local mesh refinement device - which are the main components of an adaptive PDE code. Without use of standard multigrid techniques, the same kind of computational complexity is achieved - independent of any uniformity restrictions on the applied meshes. In addition, the method is extremely simple and all computations are purely local - making the method particularly attractive in view of parallel computing. The algorithmic approach is illustrated by a well-known critical test problem. {\bf Keywords:} finite elements, hierarchical basis, adaptive mesh refinement, preconditioned conjugate gradient methods.

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Metadaten
Author:Peter Deuflhard, P. Leinen, Harry Yserentant
Document Type:ZIB-Report
Tag:adaptive mesh refinement; finite elements; hierarchical basis; preconditioned conjugate gradient methods
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F10 Iterative methods for linear systems [See also 65N22]
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N20 Ill-posed problems
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N50 Mesh generation and refinement
Date of first Publication:1988/07/28
Series (Serial Number):ZIB-Report (SC-88-05)
ZIB-Reportnumber:SC-88-05
Published in:Appeared in: IMPACT Comp. Sci. Eng. 1, pp. 3-35 (1989)
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