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A C0-Collocation-like method for elliptic equations on rectangular regions

Published online by Cambridge University Press:  17 February 2009

Zbigniew Leyk
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Abstract

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We describe a C0-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 hr(r ≥ 1) in the H1–norm and hr+1(r ≥ 2) in the L2–norm, if the collocation solution js 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.

Type
Research Article
Information
The ANZIAM Journal , Volume 38 , Issue 3 , January 1997 , pp. 368 - 387
Copyright
Copyright © Australian Mathematical Society 1997

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