Author(s)

Gelaw Temesgen Mekuria¹, Jakkula Anand Rao²

¹Department of Mathematics, Mizan Tepi University, Mizan Teferi, Ethiopia.
²Department of Mathematics, Osmania University, Hyderabad, India.

This paper examines the numerical solution of the convection-diffusion equation in 2-D. The solution of this equation possesses singularities in the form of boundary or interior layers due to non-smooth boundary conditions. To overcome such singularities arising from these critical regions, the adaptive finite element method is employed. This scheme is based on the streamline diffusion method combined with Neumann-type posteriori estimator. The effectiveness of this approach is illustrated by different examples with several numerical experiments.

Convection-Diffusion Problem, Streamline Diffusion Finite Element Method, Boundary and Interior Layers, A Posteriori Error Estimators, Adaptive Mesh Refinement

Mekuria, G. and Rao, J. (2016) Adaptive Finite Element Method for Steady Convection-Diffusion Equation. American Journal of Computational Mathematics, 6, 275-285. doi: 10.4236/ajcm.2016.63029.