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

Jin, Bangti; Lazarov, Raytcho; Pasciak, Joseph; Zhou, Zhi

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

Type

Book Chapter

Authors

Jin, Bangti
Lazarov, Raytcho
Pasciak, Joseph
Zhou, Zhi

KAUST Grant Number

KUS-C1-016-04

Date

2013

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 L2- and H1-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.

Citation

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. Numerical Analysis and Its Applications: 24–37. Available: http://dx.doi.org/10.1007/978-3-642-41515-9_3.

Acknowledgements

The research of R. Lazarov and Z. Zhou was supportedin parts by US NSF Grant DMS-1016525 and J. Pasciak has been supported byNSF Grant DMS-1216551. The work of all authors has been supported also byAward No. KUS-C1-016-04, made by King Abdullah University of Science andTechnology (KAUST)