Discretization of integro-differential equations modeling dynamic fractional order viscoelasticity

Authors:
K. Adolfsson;M. Enelund;S. Larsson;M. Racheva
Affiliations:
Dept. of Appl. Mech., Chalmers Univ. of Technology, Göteborg, Sweden;Dept. of Appl. Mech., Chalmers Univ. of Technology, Göteborg, Sweden;Dept. of Mathematics, Chalmers Univ. of Technology, Göteborg, Sweden;Dept. of Mathematics, Technical University of Gabrovo, Gabrovo, Bulgaria
Venue:
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
Year:
2005

Citing 3
Cited 0

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Abstract

We study a dynamic model for viscoelastic materials based on a constitutive equation of fractional order. This results in an integro-differential equation with a weakly singular convolution kernel. We discretize in the spatial variable by a standard Galerkin finite element method. We prove stability and regularity estimates which show how the convolution term introduces dissipation into the equation of motion. These are then used to prove a priori error estimates. A numerical experiment is included.