Some Open Questions in the Numerical Analysis of Singularly Perturbed Differential Equations

Abstract

AbstractSeveral open questions in the numerical analysis of singularly perturbed differential equations are discussed. These include whether certain convergence results in various norms are optimal, when supercloseness is obtained in finite element solutions, the validity of defect correction in finite difference approximations, and desirable adaptive mesh refinement results that remain to be proved or disproved.