Finite Element Methods for a System of Dispersive Equations

Jerry L. Bona, Hongqiu Chen, Ohannes Karakashian, Michael M. Wise

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


The present study is concerned with the numerical approximation of periodic solutions of systems of Korteweg–de Vries type, coupled through their nonlinear terms. We construct, analyze and numerically validate two types of schemes that differ in their treatment of the third derivatives appearing in the system. One approach preserves a certain important invariant of the system, up to round-off error, while the other, somewhat more standard method introduces a measure of dissipation. For both methods, we prove convergence of a semi-discrete approximation and highlight differences in the basic assumptions required for each. Numerical experiments are also conducted with the aim of ascertaining the accuracy of the two schemes when integrations are made over long time intervals.
Original languageEnglish (US)
Pages (from-to)1371-1401
Number of pages31
JournalJournal of Scientific Computing
Issue number3
StatePublished - Jul 4 2018
Externally publishedYes

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Theoretical Computer Science
  • Software
  • Engineering(all)


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