부산대학교 도서관

Summary: ``We consider a linear singularly perturbed elliptic equation on a bounded domain in ${\bf R}^n$. 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 finite elements. For globally directed transport fields we establish a new type of anisotropic a~priori estimate for the solution. In the case of $\Omega=(0,1)^2$ 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 fitted method on rectangular grids.''