The problem of selecting the shape functions for a p-type finite element. (English) Zbl 0705.73246

Babuška, I.; Griebel, M.; Pitkäranta, J.

Int. J. Numer. Methods Eng. 28, No. 8, 1891-1908 (1989).

Summary: The paper addresses the question of the optimal selection of the shape functions for p-type finite elements and discusses the effectivity of the conjugate gradient and multilevel iteration method for solving the corresponding linear system.

MSC:

74S05

Finite element methods applied to problems in solid mechanics

Keywords:

superelement; conjugate gradient; multilevel iteration method; linear system

References:

[1]	and , ’Some aspects of parallel implementation of the finite element method on message passing architectures’, University of Maryland, Computer Science Tech. Report, UMIACS-TR-88-35, CS-TR-2030. · Zbl 0693.65077
[2]	and , ’Parallel implementation of the conjugate gradient for the p-version of finite elements’, to appear.
[3]	and , ’Multilevel solution method for the p-version of finite elements, parallel implementation and comparison with other solution methods’, IBM Kingston Tech. Report KGN-137, 1988.
[4]	and , ’Parallel implementation of a multigrid method on the experimental LCAP Supercomputer II’, IBM Kingston Tech. Report KGN-155, 1987.
[5]	The Finite Element Method for Elliptic Problems, North Holland, Amsterdam, 1978.
[6]	and , ’Construction of preconditions for elliptic problems by substructurings IV’, Report BNL-40820, Brookhaven National Laboratory, 1988.
[7]	, and , ’The conjugate gradient method for the p-version of the finite element method’, to appear.
[8]	’Solution of linear systems of equations: Iterative methods’, in Sparse Matrix Techniques (Lecture Notes in Mathematics No. 572), 1977, pp. 2-49.
[9]	Multigrid Methods and Applications, Springer-Verlag, New York, 1981.