An h-p version of the continuous Petrov-Galerkin method for Volterra delay-integro-differential equations

We consider an h-p version of the continuous Petrov-Galerkin time stepping method for Volterra integro-differential equations with proportional delays. We derive a priori error bounds in the L2-, H1- and L∞-norm that are explicit in the local time steps, the local approximation orders, and the local regularity of the exact solution. Numerical experiments are presented to illustrate the theoretical results.