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)


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.


Finite Element Method Discontinuous Galerkin Method Finite Element Space Interior Penalty Local Discontinuous Galerkin Method 
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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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