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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)

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 ⊂ 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.

Keywords

Initial Data Ratio Rate Galerkin Finite Element Method Smooth Initial Data Volume Element Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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