hp-Adaptive least squares spectral element method for hyperbolic partial differential equations

  • Authors:

  • Árpád Galvão;Marc Gerritsma;Bart De Maerschalck

  • Affiliations:

  • Department of Aerospace Engineering, Delft University of Technology, Kluyverweg 1, 2629 HS Delft, The Netherlands;Department of Aerospace Engineering, Delft University of Technology, Kluyverweg 1, 2629 HS Delft, The Netherlands;Von Karman Institute for Fluid Dynamics, Waterloosesteenweg 72, 1640 Sint Genesius, Belgium

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2008

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Abstract

This paper describes a hp-adaptive spectral element formulation which is used to discretize the weak formulation obtained by minimizing the residuals in the L^2-norm. The least-squares error indicator will be briefly discussed. Refinement of the numerical approximation is based on an estimate of the regularity of the underlying exact solution; if the underlying exact solution is sufficiently smooth polynomial enrichment is employed, in areas with limited regularity h-refinement is used. For this purpose the Sobolev regularity is estimated. Functionally and geometrically non-conforming neighbouring elements are patched together using so-called mortar elements. Results of this approach are compared to uniform h- and p-refinement for a linear advection equation.