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Research Report MRR95-037

A C0 Collocation Like Method For Elliptic Equations On Rectangular Regions

Zbigniew Leyk

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 $h^{r} (r\ge 1)$ in the $H^{1}$ -norm and $h^{r+1} (r\ge 2)$ in the $L^2$ -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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