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

The analysis of singular perturbed differential equations began early in the twentieth
century, when approximate solutions were constructed from asymptotic expansions …

Two decades ago when we wrote Spectral Methods in Fluid Dynamics (1988), the subject
was still fairly novel. Motivated by the many favorable comments we have received and the …

The mathematization of all sciences, the fading of traditional scientific boundaries, the
impact of computer technology, the growing importance of computer modelling and the …

This article describes the Variational Multiscale Method (VMS) applied to flow problems. The
main idea of the formulation in the case of stationary linear problems is explained with some …

Numerical studies of stabilized finite element methods for solving scalar time-dependent
convection–diffusion–reaction equations with small diffusion are presented in this paper …

Suppressing spurious oscillations is crucial for designing reliable high-order numerical
schemes for hyperbolic conservation laws, yet it has been a challenge actively investigated …

The variational multiscale method is reviewed as a framework for develo** computational
methods for large-eddy simulation of turbulent flow. In contrast to other articles reviewing this …

The numerical solution of the non-stationary, incompressible Navier–Stokes model can be
split into linearized auxiliary problems of Oseen type. We present in a unique way different …

In this paper the grad–div stabilization for the incompressible Navier–Stokes finite element
approximations is considered from two different viewpoints:(i) as a variational multiscale …