A collocation-𝐻⁻¹-Galerkin method for some elliptic equations

Nakao, Mitsuhiro

doi:10.1090/S0025-5718-1984-0736444-7

A collocation-$H^{-1}$-Galerkin method for some elliptic equations
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Math. Comp. 42 (1984), 417-426 Request permission

Abstract:

A collocation-${H^{ - 1}}$-Galerkin method is defined for some elliptic boundary value problems on a rectangle. The method uses tensor products of discontinuous piecewise polynomial spaces and collocation based on Jacobi points with weight function ${x^2}{(1 - x)^2}$. Optimal order of ${L^2}$ rates of convergence is established for the approximation solution. A numerical example which confirms these results is presented.

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