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

Julia Brunken, Kathrin Smetana, Karsten Urban

    Research output: Contribution to journalArticleAcademicpeer-review

    3 Citations (Scopus)
    73 Downloads (Pure)

    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
    Number of pages30
    JournalSIAM journal on scientific computing
    Volume41
    Issue number1
    DOIs
    Publication statusPublished - 14 Feb 2019

    Fingerprint

    Petrov-Galerkin Method
    Galerkin methods
    Transport Equation
    Stabilization
    First-order
    Experiments
    Reduced Basis Methods
    Adjoint Operator
    Reduced Model
    Variational Formulation
    Greedy Algorithm
    Numerical Experiment
    Demonstrate

    Keywords

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

    Cite this

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    (Parametrized) First Order Transport Equations: Realization of Optimally Stable Petrov-Galerkin Methods. / Brunken, Julia; Smetana, Kathrin ; Urban, Karsten.

    In: SIAM journal on scientific computing, Vol. 41, No. 1, 14.02.2019, p. A592-A621.

    Research output: Contribution to journalArticleAcademicpeer-review

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    AU - Brunken, Julia

    AU - Smetana, Kathrin

    AU - Urban, Karsten

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    KW - Reduced basis methods

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