(Parametrized) First Order Transport Equations: Realization of Optimally Stable Petrov-Galerkin Methods

Julia Brunken, Kathrin Smetana, Karsten Urban

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    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
    Number of pages30
    JournalSIAM journal on scientific computing
    Issue number1
    Publication statusPublished - 14 Feb 2019



    • Linear transport equation
    • Inf-sup stability
    • Reduced basis methods

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