Shishkin meshes in the numerical solution of singularly perturbed differential equations

Dedicated to G.I. Shishkin on the occasion of his 70th birthday. Abstract. This article reviews some of the salient features of the piecewise-uniform Shishkin mesh. The central analytical techniques involved in the as-sociated numerical analysis are explained via a particular class of singularly perturbed differential equations. A detailed discussion of the Shishkin solution decomposition is included. The generality of the numerical approach intro-duced by Shishkin is highlighted. The impact of Shishkin’s ideas on the field of singularly perturbed differential is assessed in this selective review of his research output over the past thirty years