A conservative finite element method for the Korteweg-deVries equation

Author:
Ragnar Winther

Journal:
Math. Comp. **34** (1980), 23-43

MSC:
Primary 65N30; Secondary 35Q20

MathSciNet review:
551289

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Abstract: A finite element method for the 1-periodic Korteweg-de Vries equation

**[1]**S. AGMON,*Lectures on Elliptic Boundary Value Problems*, Van Nostrand, New York, 1965. MR**0178246 (31:2504)****[2]**M. E. ALEXANDER & J. L. MORRIS, "Galerkin methods applied to some model equations for non-linear dispersive waves,"*J. Computational Phys*. (To appear.) MR**530003 (80c:76006)****[3]**J. L. BONA & R. SMITH, "The initial-value problem for the Korteweg-de Vries equation,"*Philos. Trans. Roy. Soc. London Ser. A*, v. 278, 1975, pp. 555-604. MR**0385355 (52:6219)****[4]**J. H. BRAMBLE & J. E. OSBORN, "Rate of convergence estimates for nonselfadjoint eigenvalue approximations,"*Math. Comp.*, v. 27, 1973, pp. 525-549. MR**0366029 (51:2280)****[5]**B. FORNBERG & G. B. WHITHAM, "A numerical and theoretical study of certain nonlinear wave phenomena,"*Philos. Trans. Roy. Soc. London Ser. A*, v. 289, 1978, pp. 373-404. MR**497916 (80i:35156)****[6]**F. TAPPERT,*Numerical Solutions of the Korteweg-de Vries Equation and Its Generalizations by the Split-Step Fourier Method*, Lectures in Appl. Math., vol. 15, Amer. Math. Soc., Providence, R. I., 1974, pp. 215-216.**[7]**A. C. VLIEGENTHART, "Finite-difference methods for the Korteweg-de Vries equation,"*J. Engrg. Math.*, v. 5, 1971, pp. 137-155. MR**0363153 (50:15591)****[8]**L. B. WAHLBIN, "A dissipative Galerkin method for the numerical solution of first order hyperbolic equations,"*Mathematical Aspects of Finite Elements in Partial Differential Equations*(C. de Boor, Ed.), Academic Press, New York, 1974, pp. 147-169. MR**0658322 (58:31929)****[9]**G. B. WHITHAM,*Linear and Nonlinear Waves*, Wiley, New York, 1974. MR**0483954 (58:3905)**

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DOI:
https://doi.org/10.1090/S0025-5718-1980-0551289-5

Article copyright:
© Copyright 1980
American Mathematical Society