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- Adolfsson, Klas, 1972, et al.
(författare)
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Discretization of integro-differential equations modeling dynamic fractional order viscoelasticity
- 2006
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Ingår i: Lecture Notes in Computer Science, Springer, ''Proceedings of Large-Scale Scientific Computations, 2005, Sozopol, Bulgaria'', I. Lirkov, S. Margenov, and J. Wasniewski (Eds.). - 3540319948 ; 3743, s. 76-83
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Konferensbidrag (refereegranskat)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.
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- Enelund, Mikael, 1965, et al.
(författare)
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Space-time discretization of an integro-differential equation modeling quasi-static fractional-order viscoelasticity
- 2008
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Ingår i: J. Vib. Control. - 1077-5463. ; 14:9-10, s. 1631-1649
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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