An elliptic singularly perturbed problem with two parameters II: Robust finite element solution

A Globally Uniformly Convergent Finite Element Method for a Singularly Perturbed Elliptic Problem in Two Dimensions

We analyze a new Galerkin finite element method for numerically solving a linear convection-dominated convection-diffusion problem in two dimensions. The method is shown to be convergent, uniformly in the perturbation i ii parameter, of order h ' in a global energy norm which is stronger than the L norm. This order is optimal in this norm for our choice of trial functions.

Robust Local Problem Error Estimation for a Singularly Perturbed Problem on Anisotropic Finite Element Meshes

Singularly perturbed problems often yield solutions with strong directional features, e.g. with boundary layers. Such anisotropic solutions lend themselves to adapted, anisotropic discretizations. The quality of the corresponding numerical solution is a key issue in any computational simulation. To this end we present a new robust error estimator for a singularly perturbed reaction–diffusion pr...

Finite element methods for a singularly perturbed transmission problem

We consider a one-dimensional singularly perturbed transmission problem with two different diffusion coefficients. The solution will contain boundary layers only in the part of the domain where the diffusion coefficient is high. We derive and analyze various finite element approaches for the approximation of the solution and conduct numerical computations that show the robustness (or lack there...

A Global Uniformly Convergent Finite Element Method for a Quasilinear Singularly Perturbed Elliptic Problem

Finite difference scheme for singularly perturbed convection- diffusion problem with two small parameters

In this article a numerical method involving classical finite difference scheme on non-uniform grid is constructed for a singularly perturbed convection-diffusion boundary value problem with two small parameters affecting the convection and diffusion terms. The scheme has been analyzed for uniform convergence with respect to both singular perturbation parameters. To support the theoretical erro...