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

This article outlines the research on the application of the variational multiscale theory
(VMS) to a posteriori error estimation. VMS theory was initially developed by Professor …

Several open questions in the numerical analysis of singularly perturbed differential
equations are discussed. These include whether certain convergence results in various …

The present study deals with the finite element discretization of nanofluid convective
transport in an enclosure with variable properties. We study the Buongiorno model, which …

In this work we present a general error estimator for the finite element solution of solid
mechanics problems based on the Variational Multiscale method. The main idea is to …

An adaptive algorithm for the numerical simulation of time-dependent convection–diffusion–
reaction equations will be proposed and studied. The algorithm allows the use of the natural …

There is a wide range of stabilized finite element methods for stationary and nonstationary
convection–diffusion equations such as streamline diffusion methods, local projection …

Mixing-limited reactions are central to a wide range of processes in natural and engineered
porous media. Recent advances have shown that concentration gradients sustained by flow …

As we know, the variational multiscale element free Galerkin (VMEFG) method may still
suffer from non-physical oscillations near the boundary or interior layers when solving the …

This article deals with the residual-based a posteriori error estimation in the standard energy
norm for the streamline-diffusion finite element method (SDFEM) for singularly perturbed …