Convergence of an explicit upwind finite element method to multi-dimensional conservation laws

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Abstract

An explicit upwind finite element method is given for the numerical computation to multi-dimensional scalar conservation laws. It is proved that this scheme is consistent to the equation and monotone, and the approximate solution satisfies discrete entropy inequality. To guarantee the limit of approximate solutions to be a measure valued solution, we prove an energy estimate. Then the Lp strong convergence of this scheme is proved.

Original languageEnglish (US)
Pages (from-to)87-100
Number of pages14
JournalJournal of Computational Mathematics
Volume19
Issue number1
StatePublished - Jan 1 2001

All Science Journal Classification (ASJC) codes

  • Computational Mathematics

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