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arXiv · 1803.06925

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

Julia Brunken·Kathrin Smetana·Karsten Urban
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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.

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Julia Brunken, Kathrin Smetana, Karsten Urban. 2018-03-19. (Parametrized) First Order Transport Equations: Realization of Optimally Stable Petrov-Galerkin Methods. https://doi.org/10.1137/18m1176269

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