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

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
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[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.
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[9] Multigrid Methods and Applications, Springer-Verlag, New York, 1981.
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