The continuous Galerkin method for an integro-differential equation modeling dynamic fractional order viscoelasticity
Artikel i vetenskaplig tidskrift, 2010
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.
finite element
weakly singular kernel
stability
continuous Galerkin
a priori error estimate
linear viscoelasticity
fractional calculus
Författare
Stig Larsson
Göteborgs universitet
Chalmers, Matematiska vetenskaper, Matematik
Fardin Saedpanah
Göteborgs universitet
Chalmers, Matematiska vetenskaper, Matematik
IMA Journal of Numerical Analysis
0272-4979 (ISSN) 1464-3642 (eISSN)
Vol. 30 4 964-986Ämneskategorier
Beräkningsmatematik
DOI
10.1093/imanum/drp014