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hp-DGFEM for Partial Differential Equations with Nonnegative Characteristic Form

by E. Süli and Ch. Schwab and P. Houston

(Report number 1999-13)

Abstract
We develop the error analysis for the hp-version of a discontinuous finite element approximation to second-order partial differential equations with nonnegative 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:

@Techreport{SSH99_248,
  author = {E. S\"uli and Ch. Schwab and P. Houston},
  title = {hp-DGFEM for Partial Differential Equations with Nonnegative Characteristic Form},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1999-13},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1999/1999-13.pdf },
  year = {1999}
}

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