Discontinuous Galerkin method for an integro-differential equation modeling dynamic fractional order viscoelasticity

TL;DR

This paper develops a discontinuous Galerkin method for solving an integro-differential equation modeling fractional viscoelasticity, providing stability and error estimates, and demonstrating effectiveness through numerical examples.

Contribution

It introduces a novel discontinuous Galerkin approach for fractional viscoelasticity equations with proven stability and optimal error estimates.

Findings

The method is stable under certain conditions.

Optimal order a priori error estimates are established.

Numerical examples confirm theoretical results.

Abstract

An integro-differential equation, modeling dynamic fractional order viscoelasticity, with a Mittag-Leffler type convolution kernel is considered. A discontinuous Galerkin method, based on piecewise constant polynomials is formulated for temporal semidiscretization of the problem. Stability estimates of the discrete problem are proved, that are used to prove optimal order a priori error estimates. The theory is illustrated by a numerical example.