The contents of this paper is twofold. First, important recent results concerning finite element
methods for convection-dominated problems and incompressible flow problems are …

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 …

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 …

Many mathematical models of continuum mechanics are derived from integral conservation
laws. Examples of such models include the Euler and Navier–Stokes equations of fluid …

In this paper, we propose and analyze a local projection stabilization virtual element method
for steady scalar convection-diffusion-reaction problem in the convective-dominated regime …

A finite element error analysis of a local projection stabilization (LPS) method for the time-
dependent Navier–Stokes equations is presented. The focus is on the high-order term-by …

We propose a way to maintain strong consistency and perform error analysis in the context
of dissipation-based WENO stabilization for continuous and discontinuous Galerkin …

The concern of this manuscript is stabilized finite element simulations of two-dimensional
incompressible and viscous magnetohydrodynamic (MHD) duct flows governed by a …

The aim of this work is to design monotonicity-preserving stabilized finite element
techniques for transport problems as a blend of linear and nonlinear (shock-capturing) …

In this paper, the semilinear convection–diffusion–reaction equation is split into a lower-
order system by introducing the auxiliary variable q= a (x) ux. An H 1-Galerkin space-time …