Volume 10, Number 4, Winter 2002
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.