(Parametrized) first order transport equations: Realization of optimally stable Petrov-Galerkin methods

Julia Brunken, Kathrin Smetana, Karsten Urban

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

Abstract

We consider ultraweak variational formulations for (parametrized) linear first order transport equations in time and/or space. Computationally feasible pairs of optimally stable trial and test spaces are presented, starting with a suitable test space and defining an optimal trial space by the application of the adjoint operator. As a result, the inf-sup constant is one in the continuous as well as in the discrete case and the computational realization is therefore easy. In particular, regarding the latter, we avoid a stabilization loop within the greedy algorithm when constructing reduced models within the framework of reduced basis methods. Several numerical experiments demonstrate the good performance of the new method.

Original languageEnglish
Pages (from-to)A592-A621
JournalSIAM Journal on Scientific Computing
Volume41
Issue number1
DOIs
StatePublished - 2019

Keywords

  • inf-sup stability
  • linear transport equation
  • reduced basis methods

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