TY - JOUR
T1 - (Parametrized) first order transport equations
T2 - Realization of optimally stable Petrov-Galerkin methods
AU - Brunken, Julia
AU - Smetana, Kathrin
AU - Urban, Karsten
N1 - Publisher Copyright:
©2019 Society for Industrial and Applied Mathematics.
PY - 2019
Y1 - 2019
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 - inf-sup stability
KW - linear transport equation
KW - reduced basis methods
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U2 - 10.1137/18M1176269
DO - 10.1137/18M1176269
M3 - Article
AN - SCOPUS:85062599990
SN - 1064-8275
VL - 41
SP - A592-A621
JO - SIAM Journal on Scientific Computing
JF - SIAM Journal on Scientific Computing
IS - 1
ER -