A direct global superconvergence analysis for Sobolev and viscoelasticity type equations (Q1265606)

The first part of the paper contains a numerical analysis of a superconvergence phenomenon which arises when solving an evolution partial differential equation of Sobolev type by the finite element method. The authors prove a global superconvergence over a rectangular domain provided the true solution is sufficiently smooth. A similar technique is used to prove a global superconvergence for a viscoelasticity type evolution equation. Continuous and piecewise bilinear functions are employed over uniform partitions.