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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Quadrature-Galerkin approximations to solutions of elliptic differential equations


Author: Martin H. Schultz
Journal: Proc. Amer. Math. Soc. 33 (1972), 511-515
MSC: Primary 65N30
DOI: https://doi.org/10.1090/S0002-9939-1972-0315919-2
MathSciNet review: 0315919
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Abstract: In practice the Galerkin method for solving elliptic partial differential equations yields equations involving certain integrals which cannot be evaluated analytically. Instead these integrals are approximated numerically and the resulting equations are solved to give ``quadrature-Galerkin approximations'' to the solution of the differential equation. Using a technique of J. Nitsche, $ {L^2}$ a priori error bounds are obtained for the difference between the solution of the differential equation and a class of quadrature-Galerkin approximations.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0315919-2
Keywords: Galerkin method, quadrature, approximation, elliptic, partial differential equation
Article copyright: © Copyright 1972 American Mathematical Society