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Mathematics of Computation

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

Author: Mitsuhiro Nakao
Journal: Math. Comp. 42 (1984), 417-426
MSC: Primary 65N30
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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Article copyright: © Copyright 1984 American Mathematical Society