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 4 964-986

Subject Categories

Computational Mathematics

DOI

10.1093/imanum/drp014