A temporally adaptive hybridized discontinuous Galerkin method for time-dependent compressible flows

Alexander Jaust; Jochen Schütz

A temporally adaptive hybridized discontinuous Galerkin method for time-dependent compressible flows

Numerical Analysis 2014-06-03 v1

Authors: Alexander Jaust , Jochen Schütz

Abstract

The potential of the hybridized discontinuous Galerkin (HDG) method has been recognized for the computation of stationary flows. Extending the method to time-dependent problems can, e.g., be done by backward difference formulae (BDF) or diagonally implicit Runge-Kutta (DIRK) methods. In this work, we investigate the use of embedded DIRK methods in an HDG solver, including the use of adaptive time-step control. Numerical results demonstrate the performance of the method for both linear and nonlinear (systems of) time-dependent convection-diffusion equations.

Keywords

hybridized discontinuous galerkin method time-dependent compressible flows adaptive time-step control embedded dirk methods convection-diffusion equations hdg solver

Cite

@article{arxiv.1406.0314,
  title  = {A temporally adaptive hybridized discontinuous Galerkin method for time-dependent compressible flows},
  author = {Alexander Jaust and Jochen Schütz},
  journal= {arXiv preprint arXiv:1406.0314},
  year   = {2014}
}

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