We are interested in the approximation of partial differential equations with a data-driven
approach based on the reduced basis method and machine learning. We suppose that the …

For incompressible flow models, the pressure term serves as a Lagrange multiplier to
ensure that the incompressibility constraint is satisfied. In engineering applications, the …

We propose a novel artificial compression, reduced order model (AC-ROM) for the
numerical simulation of viscous incompressible fluid flows. The new AC-ROM provides …

In this work, we consider the spatial homogenization of a coupled transport and fluid–
structure interaction model, to the end of deriving a system of effective equations describing …

Accurate error estimation is crucial in model order reduction, to obtain small reduced-order
models as well as to certify their accuracy when deployed in downstream applications such …

In this paper we apply a reduced basis framework for the computation of flow bifurcation
(and stability) problems in fluid dynamics. The proposed method aims at reducing the …

One of the biggest challenges in Computational Geosciences is finding ways of efficiently
simulating high-dimensional problems. In this paper, we demonstrate how the RB method …

In this work, we analyze space-time reduced basis methods for the efficient numerical
simulation of hæmodynamics in arteries. The classical formulation of the reduced basis (RB) …

A reduced basis Darcy–Stokes finite element heterogeneous multiscale method (RB-DS-FE-
HMM) is proposed for the Stokes problem in porous media. The multiscale method is based …

In this paper we propose a new, purely algebraic, Petrov–Galerkin reduced basis (RB)
method to solve the parametrized Stokes equations, where parameters serve to identify the …