Optimal error estimates for Galerkin approximations to solutions of two-point boundary value problems

Authors:
Jim Douglas, Todd Dupont and Lars Wahlbin

Journal:
Math. Comp. **29** (1975), 475-483

MSC:
Primary 65L10

MathSciNet review:
0371077

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Abstract: A priori error estimates in the maximum norm are derived for Galerkin approximations to solutions of two-point boundary value problems. The class of Galerkin spaces considered includes almost all (quasiuniform) piecewise-polynomial spaces that are used in practice. The estimates are optimal in the sense that no better rate of approximation is possible in general in the spaces employed.

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DOI:
https://doi.org/10.1090/S0025-5718-1975-0371077-0

Article copyright:
© Copyright 1975
American Mathematical Society