Space-time discretization of an integro-differential equation modeling quasi-static fractional-order viscoelasticity
Journal article, 2008

We study a quasi-static model for viscoelastic materials based on a constitutive equation of fractional order. In the quasi-static case this results in a Volterra integral equation of the second kind, with a weakly singular kernel in the time variable, and which also involves partial derivatives of second order in the spatial variables. We discretize by means of a discontinuous Galerkin finite element method in time and a standard continuous Galerkin finite element method in space. To overcome the problem of the growing amount of data that has to be stored and used at each time step, we introduce sparse quadrature in the convolution integral. We prove a priori and a posteriori error estimates, which can be used as the basis for an adaptive strategy.

Finite element • discontinuous Galerkin • weakly singular kernel • error estimate • a priori • a posteriori • sparse quadrature • adaptivity.

Author

Mikael Enelund

Dynamics

Stig Larsson

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Klas Adolfsson

Dynamics

JVC/Journal of Vibration and Control

1077-5463 (ISSN)

Vol. 14 9-10 1631-1649

Subject Categories

Computational Mathematics

More information

Created

10/7/2017