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


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
Full Text: DOI EuDML


[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
[3] de Boor, C.: On local spline approximation by moments. J. Math. Mech.17, 729-735 (1968) · Zbl 0162.08402
[4] Douglas, J., Dupont, T.: The effect of interpolating the coefficients in non-linear parabolic Galerkin procedures. To appear · Zbl 0311.65060
[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
[8] Ford, W.: Semidiscrete Galerkin approximations to non-linear pseudoparabolic partial differential equations. To appear in Aequationes Math.
[9] Hofsommer, D. J., van de Riet, R. P.: On the numerical calculation of elliptic integrals of the first and second kind and the elliptic functions of Jacobi. Numer. Math.5, 291-302 (1963) · Zbl 0123.13204 · doi:10.1007/BF01385899
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.