Galerkin FEM for Fractional Order Parabolic Equations with Initial Data in H− s, 0 ≤ s ≤ 1

  • Bangti Jin
  • Raytcho Lazarov
  • Joseph Pasciak
  • Zhi Zhou
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8236)


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.


Initial Data Ratio Rate Galerkin Finite Element Method Smooth Initial Data Volume Element Method 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Bangti Jin
    • 1
  • Raytcho Lazarov
    • 1
  • Joseph Pasciak
    • 1
  • Zhi Zhou
    • 1
  1. 1.Department of MathematicsTexas A&M UniversityCollege StationUSA

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