ON CONVERGENCE OF THE FINITE ELMENT METHOD FOR DYNAMIC FRACTIONAL ORDER VISCOELASTICITY

The standard Galerkin finit element method for spatial discretization of an integro-differential equation is studied. The model problem arises in the theory of fractional order viscoelasticity, which has a memory term with a kernel of positive type. Optimal order L1(L2) and L1(H1), priori error estimates, for the finite element approximation of the solution are obtained.