UNSTRUCTURED GRID ADAPTATION FOR CONVECTION-DOMINATED SEMICONDUCTOR EQUATIONS

A. EL BOUKILI, A. MADRANE AND R. VAILLANCOURT

Abstract. A Raviart-Thomas mixed finite element is used to develop new a posteriori local error indicators for convection- dominated semiconductor transport equations. Lower and upper bounds of the estimators are established. These bounds differ by a negative power, h^-1/2, of the mesh size. Existence and uniqueness of the solution in the continuous and discrete cases are proven. The anisotropy of the H(div) norm and the poor regularity of H(div) functions prevent a direct application of frequently used arguments. An optimal estimator is obtained using a rigorous nonstandard analysis. Numerical results in the case of a realistic device show that an unstructured grid adaptation based on these estimators leads to an efficient and robust algorithm.