Error Estimates for Three-Dimensional Singularly Perturbed Convection-Diffusion Problem

Abstract

The main aim of the present work is to propose a posteriori error estimates for singularly perturbed convection-diffusion problem in three-dimensions. It has been observed that for small singular perturbation parameter, the problem under consideration displays nonphysical oscillations in the small subregions of the boundary layers. Hughes stabilization strategy along with the Streamline upwind/Petrov-Galerkin (SUPG) method has been proposed to approximate the solution of the problem. Reliable a posteriori error estimates in energy norm on anisotropic meshes have been developed for the proposed method.