Discontinuous Galerkin method for an integro-differential equation modeling dynamic fractional order viscoelasticity
Provides a rigorous numerical analysis for a specific class of fractional viscoelasticity models, but the method is incremental (piecewise constant polynomials) and the impact is limited to the domain of fractional PDEs.
The paper develops a discontinuous Galerkin method for temporal discretization of an integro-differential equation modeling dynamic fractional order viscoelasticity, proving stability and optimal order a priori error estimates, with numerical validation.
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.