Abstract
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 ⊂ ℝd, 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.
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Jin, B., Lazarov, R., Pasciak, J., Zhou, Z. (2013). Galerkin FEM for Fractional Order Parabolic Equations with Initial Data in H − s, 0 ≤ s ≤ 1. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Numerical Analysis and Its Applications. NAA 2012. Lecture Notes in Computer Science, vol 8236. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41515-9_3
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DOI: https://doi.org/10.1007/978-3-642-41515-9_3
Publisher Name: Springer, Berlin, Heidelberg
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