Abstract
| Original language | English |
|---|---|
| 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 |
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Keywords
- Linear transport equation
- Inf-sup stability
- Reduced basis methods
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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 journal › Article › Academic › peer-review
TY - JOUR
T1 - (Parametrized) First Order Transport Equations: Realization of Optimally Stable Petrov-Galerkin Methods
AU - Brunken, Julia
AU - Smetana, Kathrin
AU - Urban, Karsten
PY - 2019/2/14
Y1 - 2019/2/14
N2 - 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.
AB - 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.
KW - Linear transport equation
KW - Inf-sup stability
KW - Reduced basis methods
UR - http://www.scopus.com/inward/record.url?scp=85062599990&partnerID=8YFLogxK
U2 - 10.1137/18M1176269
DO - 10.1137/18M1176269
M3 - Article
VL - 41
SP - A592-A621
JO - SIAM journal on scientific computing
JF - SIAM journal on scientific computing
SN - 1064-8275
IS - 1
ER -