J Austral Math Soc Ser B 38 pp368--387, 1997.

A C 0-collocation-like method for elliptic equations on rectangular regions

Zbigniew Leyk

(Received 1 November 1993; revised 31 May 1995)

Abstract

We describe a C 0-collocation-like method for solving two-dimensional elliptic Dirichlet problems on rectangular regions, using tensor products of continuous piecewise polynomials. Nodes of the Lobatto quadrature formula are taken as the points of collocation. We show that the method is stable and convergent with order h r (r ³ 1) in the H 1-norm and h r + 1 (r ³ 2) in the L2 norm, if the collocation solution is a piecewise polynomial of degree not greater than r with respect to each variable. The method has an advantage over the Galerkin procedure for the same space in that no integrals need be evaluated or approximated.

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Author

Zbigniew Leyk
SMS, Australian National University, Canberra, ACT 0200, Australia.

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