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 language | English |
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Pages (from-to) | A592-A621 |
Number of pages | 30 |
Journal | SIAM journal on scientific computing |
Volume | 41 |
Issue number | 1 |
DOIs | |
Publication status | Published - 14 Feb 2019 |
Keywords
- Linear transport equation
- Inf-sup stability
- Reduced basis methods