Discretization of Integro-Differential Equations Modeling Dynamic Fractional Order Viscoelasticity
نویسندگان
چکیده
We study a dynamic model for viscoelastic materials based on a constitutive equation of fractional order. This results in an integrodifferential equation with a weakly singular convolution kernel. We discretize in the spatial variable by a standard Galerkin finite element method. We prove stability and regularity estimates which show how the convolution term introduces dissipation into the equation of motion. These are then used to prove a priori error estimates. A numerical experiment is included.
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