Error estimates for finite element methods for scalar conservation laws

Bernardo Cockburn, Pierre Alain Gremaud

Research output: Contribution to journalArticlepeer-review

79 Scopus citations


In this paper, new a posteriori error estimates for the shock-capturing streamline diffusion (SCSD) method and the shock-capturing discontinuous galerkin (SCDG) method for scalar conservation laws are obtained. These estimates are then used to prove that the SCSD method and the SCDG method converge to the entropy solution with a rate of at least h1/8 and h1/4, respectively, in the L(L1)-norm. The triangulations are made of general acute simplices and the approximate solution is taken to be piecewise a polynomial of degree k. The result is independent of the dimension of the space.

Original languageEnglish (US)
Pages (from-to)522-554
Number of pages33
JournalSIAM Journal on Numerical Analysis
Issue number2
StatePublished - Apr 1996


  • Discontinuous galerkin method
  • Error estimates
  • Multidimensional conservation laws
  • Streamline diffusion method


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