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Efficient Preconditioning for the p-Version Finite Element Method in Two Dimensions

Parallel preconditioners are formulated and analyzed for systems of equations arising from the p-version finite element method applied to second-order self-adjoint elliptic boundary value problems in two dimensions. By using new theoretical results for polynomial spaces, it is proved that the condit...

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Bibliographic Details
Published in:SIAM journal on numerical analysis 1991-06, Vol.28 (3), p.624-661
Main Authors: Babuska, I., Craig, A., Mandel, J., Pitkaranta, J.
Format: Article
Language:English
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Summary:Parallel preconditioners are formulated and analyzed for systems of equations arising from the p-version finite element method applied to second-order self-adjoint elliptic boundary value problems in two dimensions. By using new theoretical results for polynomial spaces, it is proved that the condition number of the preconditioned system grows as log2p, where p is the degree of the polynomial space. Numerical results are presented showing that the condition number indeed grows very slowly with p.
ISSN:0036-1429
1095-7170
DOI:10.1137/0728034