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Mesh refinement and iterative solution methods for finite element computations
Author(s) -
Carey Graham F.,
Humphrey David L.
Publication year - 1981
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620171110
Subject(s) - finite element method , computation , adaptive mesh refinement , computer science , a priori and a posteriori , iterative method , algorithm , nonlinear system , mathematical optimization , mathematics , extended finite element method , mesh generation , mixed finite element method , iterative and incremental development , computational science , structural engineering , engineering , philosophy , physics , epistemology , quantum mechanics , software engineering
Global and element residuals are introduced to determine a posteriori , computable, error bounds for finite element computations on a given mesh. The element residuals provide a criterion for determining where a finite element mesh requires refinement. This indicator is implemented in an algorithm in a finite element research program. There it is utilized to automatically refine the mesh for sample two‐point problems exhibiting boundary layer and interior layer solutions. Results for both linear and nonlinear problems are presented. An important aspect of this investigation concerns the use of adaptive refinement in conjunction with iterative methods for system solution. As the mesh is being enriched through the refinement process, the solution on a given mesh provides an accurate starting iterate for the next mesh, and so on. A wide range of iterative methods are examined in a feasibility study and strategies for interweaving refinement and iteration are compared.