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IMA Journal of Numerical Analysis

Year: 2010  |  Volume: 30  |  Issue: 4  |  Page No.: 964 - 986

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

S Larsson and F. Saedpanah


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.

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