A posteriori error estimates of discontinuous Galerkin methods for non-standard Volterra integro-differential equations

摘要

In this paper we establish a posteriori error estimates for the discontinuous Galerkin (DG) method applied to linear, semilinear and non-standard (non-linear) Volterra integro-differential equations. We also present an analysis of the DG method with quadrature for the memory term. Numerical experiments based on three integro-differential equations are used to illustrate various aspects of the error analysis.