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1991•SIAM Journal on Numerical AnalysisRequires access

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

Ivo M. Babuska, Alan W. Craig, Jan Mandel, Juhani Pitkäranta

Open publisher page 208 citations

Abstract

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 $\log ^2 p$, where p is the degree of the polynomial space. Numerical results are presented showing that the condition number indeed grows very slowly with p.

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What this paper is about

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 $\log ^2 p$, where p is the degree of the polynomial space. Numerical results are presented showing that the condition number indeed grows very slowly with p.

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Available abstract

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 $\log ^2 p$, where p is the degree of the polynomial space. Numerical results are presented showing that the condition number indeed grows very slowly with p.

Key concepts: Mathematics, Finite element method, Boundary value problem, Degree of a polynomial, Polynomial, Condition number, Mathematical analysis, Space (punctuation)

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