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Error estimates for a Galerkin method for a class of model equations for long waves. (English) Zbl 0283.65052


MSC:

65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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References:

[1] Benjamin, T. B., Bona, J. L., Mahoney, J. J.: Model equations for long waves in nonlinear dispersive systems. Philos. Trans. R. Soc. London, A272, 47-78 (1972) · Zbl 0229.35013 · doi:10.1098/rsta.1972.0032
[2] Benjamin, T. B., Bona, J. L.: Model equations for long waves in nonlinear dispersive systems II. To appear. · Zbl 0229.35013
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[5] Douglas, J., Dupont, T., Wahlbin, L.: OptimalL ? error estimates for Galerkin approximations to solutions of two point boundary value problems. To appear in Math. Comp. · Zbl 0306.65053
[6] Dupont, T.: Galerkin methods for first order hyperbolics: an example. SIAM J. Numer. Anal.10, 890-899 (1973) · doi:10.1137/0710074
[7] Fix, G.: Effects of quadrature errors in finite element approximation of steady state, eigenvalue and parabolic problems. Proceedings of a Symposium on the mathematical foundations of the finite element metho at the University of Maryland, June 1972. New York: Academic Press 1972 · Zbl 0282.65081
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[10] Lamb, H.: Hydrodynamics, 6th edition. New York: Dover Publications 1945 · Zbl 0828.01012
[11] Lions, J. L.: Quelques m?thodes de r?solution des probl?mes aux limites non lin?aires. Paris: Dunod 1969 · Zbl 0189.40603
[12] Nassif, N. R.: Thesis, Harvard University, 1972
[13] Nitsche, J.: Ein Kriterium f?r die Quasioptimalit?t des Ritzschen Verfahrens. Numer. Math.11, 346-348 (1968) · Zbl 0175.45801 · doi:10.1007/BF02166687
[14] Nitsche, J.: Verfahren von Ritz und Spline Interpolation bei Sturm-Liouville Randwertproblemen. Numer. Math.13, 260-265 (1969) · Zbl 0181.18204 · doi:10.1007/BF02167557
[15] Wheeler, M. F.: A prioriL 2 error estimates for Galerkin approximations to parabolic partial differential equations. SIAM J. Numer., Anal.10, 723-759 (1973) · doi:10.1137/0710062
[16] Wheeler, M. F.: An optimalL ? error estimate for Galerkin approximations to the solution of two point boundary value problems. SIAM J. Numer., Anal.10, 914-917 (1973) · Zbl 0266.65061 · doi:10.1137/0710077
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