Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8902551 | Applied Numerical Mathematics | 2018 | 18 Pages |
Abstract
We consider the numerical approximation of a time-fractional cable equation involving two Riemann-Liouville fractional derivatives. We investigate a semidiscrete scheme based on the lumped mass Galerkin finite element method (FEM), using piecewise linear functions. We establish optimal error estimates for smooth and middly smooth initial data, i.e., vâHq(Ω)â©H01(Ω), q=1,2. For nonsmooth initial data, i.e., vâL2(Ω), the optimal L2(Ω)-norm error estimate requires an additional assumption on mesh, which is known to be satisfied for symmetric meshes. A quasi-optimal Lâ(Ω)-norm error estimate is also obtained. Further, we analyze two fully discrete schemes using convolution quadrature in time based on the backward Euler and the second-order backward difference methods, and derive error estimates for smooth and nonsmooth data. Finally, we present several numerical examples to confirm our theoretical results.
Related Topics
Physical Sciences and Engineering
Mathematics
Computational Mathematics
Authors
Mariam Al-Maskari, Samir Karaa,