Non-linear Petrov-Galerkin methods for reduced order modelling of the Navier-Stokes equations using a mixed finite element pair

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Reduced-order modeling of advection-dominated systems with recurrent neural networks and convolutional autoencoders (2020, methodology): “For example, we could use intrusive methods (which project the governing equations onto the reducedbasis), as seen in [28, 29], which use a Galerkin projection or [1, 30, 31], which use the Petrov-Galerkin method (see [32] for the comparison of these two methods).”
On closures for reduced order models—A spectrum of first-principle to machine-learned avenues (2021, unknown): “Although the Petrov–Galerkin projection 248 could mitigate some of the challenges the Galerkin ROMs have to face in the under-resolved simulation of turbulent ﬂows, we limit ourselves to Galerkin projection-based ROMs in the current review, where closure models have been mainly developed to improve…”
Non-intrusive reduced order modelling of the Navier-Stokes equations (2015, methodology): “A new Petrov–Galerkin method was introduced to stabilize the resulting equations and produce more accurate results [15].”
Non‐intrusive reduced‐order modelling of the Navier–Stokes equations based on RBF interpolation (2015, methodology): “[17] presented a Petrov–Galerkin method for reduced-order modelling of the Navier–Stokes equations.”