Galerkin FEM for Fractional Order Parabolic Equations with Initial Data in H-s, 0 <= s <= 1
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We investigate semi-discrete numerical schemes based on the standard Galerkin and lumped mass Galerkin finite element methods for an initial-boundary value problem for homogeneous fractional diffusion problems with non-smooth initial data. We assume that d , d = 1,2,3 is a convex polygonal (polyhedral) domain. We theoretically justify optimal order error estimates in L 2 - and H 1 -norms for initial data in H -s (), 0 s 1. We confirm our theoretical findings with a number of numerical tests that include initial data v being a Dirac -function supported on a (d-1)-dimensional manifold. 2013 Springer-Verlag.