Computational fluid dynamics

Implementation of the reduced basis method requires the choice of a subspace and a projector onto that subspace. For an arbitrarily chosen subspace-projector pair, existence of the true solution curve is not sufficient to guarantee the existence of the corresponding reduced basis solution curve. However, when the former curve exists, it has been shown that there are infinitely many subspace-projector pairings, each utilizing an arbitrarily selected subspace, under which the reduced basis solution curve exists. Moreover, the resulting error estimates are of the same nature as those that apply in the more familiar case when a subspace is paired with its orthogonal projector.