TY - GEN
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
PY - 2013/11/7
Y1 - 2013/11/7
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.
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.
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 - Conference article published in proceeding or book
SN - 9783642415142
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 24
EP - 37
BT - Numerical Analysis and Its Applications - 5th International Conference, NAA 2012, Revised Selected Papers
T2 - 5th International Conference on Numerical Analysis and Applications, NAA 2012
Y2 - 15 June 2013 through 20 June 2013
ER -