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 Ω ⊂ ℝ 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 (Ω), 0 ≤ s ≤ 1. We confirm our theoretical findings with a number of numerical tests that include initial data v being a Dirac δ-function supported on a (d-1)-dimensional manifold. © 2013 Springer-Verlag.
author list (cited authors)
Jin, B., Lazarov, R., Pasciak, J., & Zhou, Z.
complete list of authors
Jin, Bangti||Lazarov, Raytcho||Pasciak, Joseph||Zhou, Zhi
editor list (cited editors)
Dimov, I., Faragó, I., & Vulkov, L. G.