A superconvergent finite element method for the korteweg-de vries equation

Douglas N. Arnold, Ragnar Winther

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)23-36
Number of pages14
JournalMathematics of Computation
Volume38
Issue number157
DOIs
StatePublished - Jan 1982

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