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

Nakao, Mitsuhiro

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

A collocation- $H\sp{-1}$ -Galerkin method for some elliptic equations

Author: Mitsuhiro Nakao
Journal: Math. Comp. 42 (1984), 417-426
MSC: Primary 65N30
DOI: https://doi.org/10.1090/S0025-5718-1984-0736444-7
MathSciNet review: 736444
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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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