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This contribution introduces a model order reduction approach for anadvection-reaction problem with a parametrized reaction function. Theunderlying discretization uses an ultraweak formulation with an $L^2$-liketrial space and an 'optimal' test space as introduced by Demkowicz et al. Thisensures the stability of the discretization and in addition allows for asymmetric reformulation of the problem in terms of a dual solution which canalso be interpreted as the normal equations of an adjoint least-squaresproblem. Classic model order reduction techniques can then be applied to thespace of dual solutions which also immediately gives a reduced primal space. Weshow that the necessary computations do not require the reconstruction of anyprimal solutions and can instead be performed entirely on the space of dualsolutions. We prove exponential convergence of the Kolmogorov $N$-width andshow that a greedy algorithm produces quasi-optimal approximation spaces forboth the primal and the dual solution space. Numerical experiments based on thebenchmark problem of a catalytic filter confirm the applicability of theproposed method.

Model order reduction of an ultraweak and optimally stable variational formulation for parametrized reactive transport problems