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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

**[1]**Carl de Boor,*On the convergence of odd-degree spline interpolation*, J. Approximation Theory**1**(1968), 452–463. MR**0237996****[2]**Carl de Boor,*On the local spline approximation by moments*, J. Math. Mech.**17**(1967/1968), 729–735. MR**0223803****[3]**Jim Douglas Jr. and Todd Dupont,*Galerkin approximations for the two point boundary problem using continuous, piecewise polynomial spaces*, Numer. Math.**22**(1974), 99–109. MR**0362922****[4]**J. Nitsche,*Ein Kriterium für die Quasi-Optimalität des Ritzschen Verfahrens*, Numer. Math.**11**(1968), 346–348 (German). MR**0233502****[5]**Alfred H. Schatz,*An observation concerning Ritz-Galerkin methods with indefinite bilinear forms*, Math. Comp.**28**(1974), 959–962. MR**0373326**, 10.1090/S0025-5718-1974-0373326-0**[6]**Mary Fanett Wheeler,*An optimal 𝐿_{∞} error estimate for Galerkin approximations to solutions of two-point boundary value problems*, SIAM J. Numer. Anal.**10**(1973), 914–917. MR**0343659**

Retrieve articles in *Mathematics of Computation*
with MSC:
65L10

Retrieve articles in all journals with MSC: 65L10

Additional Information

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

Article copyright:
© Copyright 1975
American Mathematical Society