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The continuous Galerkin method for an integro-differential equation modeling dynamic fractional order viscoelasticity

Stig Larsson (Institutionen för matematiska vetenskaper, matematik) ; Fardin Saedpanah (Institutionen för matematiska vetenskaper, matematik)
IMA Journal of Numerical Analysis (1464-3642). Vol. 30 (2010), 4, p. 964-986.
[Artikel, refereegranskad vetenskaplig]

We consider a fractional order integro-differential equation with a weakly singular convolution kernel. The equation with homogeneous mixed Dirichlet and Neumann boundary conditions is reformulated as an abstract Cauchy problem, and well-posedness is verified in the context of linear semigroup theory. Then we formulate a continuous Galerkin method for the problem, and we prove stability estimates. These are then used to prove a priori error estimates. The theory is illustrated by a numerical example.

Nyckelord: finite element; continuous Galerkin; linear viscoelasticity; fractional calculus; weakly singular kernel; stability; a priori error estimate



Denna post skapades 2009-08-07. Senast ändrad 2014-09-02.
CPL Pubid: 95762

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Numerisk analys

Chalmers infrastruktur