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Space-time discretization of an integro-differential equation modeling quasi-static fractional-order viscoelasticity

Mikael Enelund (Institutionen för tillämpad mekanik, Dynamik) ; Stig Larsson (Institutionen för matematiska vetenskaper, matematik) ; Klas Adolfsson (Institutionen för tillämpad mekanik, Dynamik)
J. Vib. Control (1077-5463). Vol. 14 (2008), 9-10, p. 1631-1649.
[Artikel, refereegranskad vetenskaplig]

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.

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



Denna post skapades 2008-10-06. Senast ändrad 2014-09-02.
CPL Pubid: 74871

 

Institutioner (Chalmers)

Institutionen för tillämpad mekanik, Dynamik (1900-2017)
Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Numerisk analys

Chalmers infrastruktur