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hp-DGFEM for Partial Differential Equations with Nonnegative Characteristic Form

  • Endre Süli
  • Christoph Schwab
  • Paul Houston
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 11)

Abstract

We develop the error analysis for the hp-version of a discontinuous finite element approximation to second-order partial differential equations with non-negative characteristic form. This class of equations includes classical examples of second-order elliptic and parabolic equations, first-order hyperbolic equations, as well as equations of mixed type. We establish an a priori error bound for the method which is of optimal order in the mesh size h and 1 order less than optimal in the polynomial degree p. In the particular case of a first-order hyperbolic equation the error bound is optimal in h and 1/2 an order less than optimal in p.

Keywords

Finite Element Method Discontinuous Galerkin Method Finite Element Space Interior Penalty Local Discontinuous Galerkin Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Endre Süli
    • 1
  • Christoph Schwab
    • 2
  • Paul Houston
    • 1
  1. 1.Computing LaboratoryUniversity of OxfordOxfordUK
  2. 2.Seminar for Applied MathematicsETH ZürichZürichSwitzerland

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