UNIFORM A PRIORI ESTIMATES FOR SINGULARLY PERTURBED ELLIPTIC EQUATIONS IN MULTIDIMENSIONS

We consider a linear singularly perturbed elliptic equation on a bounded domain in R n . This equation serves as a model for the interplay between the transport term and a relatively small viscosity term in some problems of mathematical physics. We establish a priori estimates that hold uniformly in the small parameter. From this one can prove an abstract a priori error estimate for the discretization with conforming nite elements. For globally directed transport elds we establish a new type of anisotropic a priori estimate for the solution. In the case of › = (0; 1) 2 we prove a priori estimates for certain higher order derivatives in isotropic as well as anisotropic norms. In a subsequent paper we will apply these results to show uniform convergence of an exponentially tted method on rectangular grids.