Finite element approximation of a time-fractional diffusion problem for a domain with a re-entrant corner
Le, Kim Ngan ; McLean, William ; Lamichhane, Bishnu
ANZIAM Journal, Tome 58 (2017), / Harvested from Australian Mathematical Society
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An initial-boundary value problem for a time-fractional diffusion equation is discretized in space, using continuous piecewise-linear finite elements on a domain with a re-entrant corner. Known error bounds for the case of a convex domain break down, because the associated Poisson equation is no longer \(H^{2}\) -regular. In particular, the method is no longer second-order accurate if quasi-uniform triangulations are used. We prove that a suitable local mesh refinement about the re-entrant corner restores second-order convergence. In this way, we generalize known results for the classical heat equation. doi:10.1017/S1446181116000365

Publié le : 2017-01-01
DOI : https://doi.org/10.21914/anziamj.v59i0.10940 
@article{10940,
     title = {Finite element approximation of a time-fractional diffusion problem for a domain with a re-entrant corner},
     journal = {ANZIAM Journal},
     volume = {58},
     year = {2017},
     doi = {10.21914/anziamj.v59i0.10940},
     language = {EN},
     url = {http://dml.mathdoc.fr/item/10940}
}

Le, Kim Ngan; McLean, William; Lamichhane, Bishnu. Finite element approximation of a time-fractional diffusion problem for a domain with a re-entrant corner. ANZIAM Journal, Tome 58 (2017) . doi : 10.21914/anziamj.v59i0.10940. http://gdmltest.u-ga.fr/item/10940/