In the present paper, a brief survey on computational techniques for the different classes of
singularly perturbed problems is given. This survey is a continuation of work performed …

In recent years, machine learning methods have been used to solve partial differential
equations (PDEs) and dynamical systems, leading to the development of a new research …

Finite element computations for singularly perturbed convection–diffusion equations have
long been an attractive theme for numerical analysis. In this article, we consider the …

In this article, we demonstrate how one can improve the numerical solution of singularly
perturbed problems involving multiple boundary layers by using a combination of analytic …

Turning points occur in many circumstances in fluid mechanics. When the viscosity is small,
very complex phenomena can occur near turning points, which are not yet well understood …

In this article, a staggered discontinuous Galerkin (SDG) approximation on rectangular
meshes for elliptic problems in two dimensions is constructed and analyzed. The optimal …

In this work, we present a novel method to approximate stiff problems using a finite volume
(FV) discretization. The stiffness is caused by the existence of a small parameter in the …

The goal of this article is to study the boundary layers of reaction–diffusion equations in a
circle and provide some numerical applications which utilize the so-called boundary layer …

In this article, we discuss reaction-diffusion problems which produce ordinary boundary
layers and elliptic corner layers. Using the classical polynomial Q 1-finite elements spaces …

In this article we discuss singularly perturbed convection–diffusion equations in a channel in
cases producing parabolic boundary layers. It has been shown that one can improve the …