Various realizations of variational multiscale (VMS) methods for simulating turbulent
incompressible flows have been proposed in the past fifteen years. All of these realizations …

Incompressible flow problems appear in many models of physical processes and
applications. Their numerical simulation requires in particular a spatial discretization. Finite …

The kinetic energy of a flow is proportional to the square of the L 2 (Ω) norm of the velocity.
Given a sufficient regular velocity field and a velocity finite element space with polynomials …

In this paper, we present a convergence analysis of a weak Galerkin finite element method
(WG-FEM) using polygonal meshes for the semilinear singularly perturbed time-dependent …

This paper presents a Streamline-Upwind Petrov–Galerkin (SUPG) reduced order model
(ROM) based on proper orthogonal decomposition (POD). This ROM is investigated …

We present new results in the numerical analysis of singularly perturbed convection‐
diffusion‐reaction problems that have appeared in the last five years. Mainly discussing …

This work extends the flux-corrected transport (FCT) methodology to arbitrary order
continuous finite element discretizations of scalar conservation laws on simplex meshes …

Abstract Galerkin and Petrov–Galerkin projection-based reduced-order models (ROMs) of
transient partial differential equations are typically obtained by performing a dimension …

We carry out a stability and convergence analysis for the fully discrete scheme obtained by
combining a finite or virtual element spatial discretization with the upwind-discontinuous …

In this work, we propose viable and efficient strategies for the stabilization of the reduced
basis approximation of an advection dominated problem. In particular, we investigate the …