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.
|Original language||English (US)|
|Title of host publication||Numerical Analysis and Its Applications|
|Number of pages||14|
|State||Published - 2013|
Bibliographical noteKAUST 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.