Discontinuous Galerkin method for an integro-differential equation modeling dynamic fractional order viscoelasticity
Journal article, 2015
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.
Integro-differential equation
Fractional order viscoelasticity
Discontinuous Galerkin method
A priori estimate
Weakly singular kernel
Stability
Author
Stig Larsson
University of Gothenburg
Chalmers, Mathematical Sciences, Mathematics
Milena Racheva
Technical University of Gabrovo
Fardin Saedpanah
University of Kurdistan
Computer Methods in Applied Mechanics and Engineering
0045-7825 (ISSN)
Vol. 283 196-209Subject Categories
Computational Mathematics
Roots
Basic sciences
DOI
10.1016/j.cma.2014.09.018