TY - CHAP

T1 - Galerkin FEM for Fractional Order Parabolic Equations with Initial Data in H − s , 0 ≤ s ≤ 1

AU - Jin, Bangti

AU - Lazarov, Raytcho

AU - Pasciak, Joseph

AU - Zhou, Zhi

N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
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)
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/598393

UR - http://link.springer.com/10.1007/978-3-642-41515-9_3

UR - http://www.scopus.com/inward/record.url?scp=84886851129&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-41515-9_3

DO - 10.1007/978-3-642-41515-9_3

M3 - Chapter

SN - 9783642415142

SP - 24

EP - 37

BT - Numerical Analysis and Its Applications

PB - Springer Nature

ER -