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Discretization of integro-differential equations modeling dynamic fractional order viscoelasticity

Klas Adolfsson (Institutionen för tillämpad mekanik, Dynamik) ; Mikael Enelund (Institutionen för tillämpad mekanik, Dynamik) ; Stig Larsson (Institutionen för matematiska vetenskaper, matematik) ; Milena Racheva
Lecture Notes in Computer Science, Springer, ''Proceedings of Large-Scale Scientific Computations, 2005, Sozopol, Bulgaria'', I. Lirkov, S. Margenov, and J. Wasniewski (Eds.) Vol. 3743 (2006), p. 76-83.
[Konferensbidrag, refereegranskat]

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.



Denna post skapades 2006-12-20. Senast ändrad 2014-09-02.
CPL Pubid: 24450

 

Institutioner (Chalmers)

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

Ämnesområden

Matematik
Fastkroppsmekanik

Chalmers infrastruktur