Optimal 𝐿_{∞} error estimates for Galerkin approximations to solutions of two-point boundary value problems

Douglas, Jim; Dupont, Todd; Wahlbin, Lars

doi:10.1090/S0025-5718-1975-0371077-0

Optimal $L_{\infty }$ error estimates for Galerkin approximations to solutions of two-point boundary value problems
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by Jim Douglas, Todd Dupont and Lars Wahlbin PDF

Math. Comp. 29 (1975), 475-483 Request permission

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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