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. 30 964-986

Ämneskategorier

Beräkningsmatematik

DOI

10.1093/imanum/drp014