The continuous Galerkin method for an integro-differential equation modeling dynamic fractional order viscoelasticity
Journal article, 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
Author
Stig Larsson
University of Gothenburg
Chalmers, Mathematical Sciences, Mathematics
Fardin Saedpanah
University of Gothenburg
Chalmers, Mathematical Sciences, Mathematics
IMA Journal of Numerical Analysis
0272-4979 (ISSN) 1464-3642 (eISSN)
Vol. 30 4 964-986Subject Categories
Computational Mathematics
DOI
10.1093/imanum/drp014