A superconvergent finite element method for the Korteweg-deVries equation

Authors:
Douglas N. Arnold and Ragnar Winther

Journal:
Math. Comp. **38** (1982), 23-36

MSC:
Primary 65M60; Secondary 76A60, 76B15

DOI:
https://doi.org/10.1090/S0025-5718-1982-0637284-8

MathSciNet review:
637284

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Abstract: An unconditionally stable fully discrete finite element method for the Korteweg-de Vries equation is presented. In addition to satisfying optimal order global estimates, it is shown that this method is superconvergent at the nodes. The algorithm is derived from the conservative method proposed by the second author by the introduction of a small time-independent forcing term into the discrete equations. This term is a form of the quasiprojection which was first employed in the analysis of superconvergence phenomena for parabolic problems. However, in the present work, unlike in the parabolic case, the quasiprojection is used as perturbation of the discrete equations and does not affect the choice of initial values.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1982-0637284-8

Article copyright:
© Copyright 1982
American Mathematical Society