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Some error estimates for the finite volume element method for a parabolic problem

Panagiotis Chatzipantelidis ; Raytcho Lazarov ; Vidar Thomée (Institutionen för matematiska vetenskaper, matematik)
Computational Methods in Applied Mathematics (1609-4840). Vol. 13 (2013), 3, p. 251-279.
[Artikel, refereegranskad vetenskaplig]

We study spatially semidiscrete and fully discrete finite volume element methods for the homogeneous heat equation with homogeneous Dirichlet boundary conditions and derive error estimates for smooth and nonsmooth initial data. We show that the results of our earlier work [Math. Comp. 81 (2012), no. 277, 1–20; MR2833485 (2012f:65159)] for the lumped mass method carry over to the present situation. In particular, in order for error estimates for initial data only in L2 to be of optimal second order for positive time, a special condition is required, which is satisfied for symmetric triangulations. Without any such condition, only first order convergence can be shown, which is illustrated by a counterexample. Improvements hold for triangulations that are almost symmetric and piecewise almost symmetric.

Nyckelord: Finite Volume Method; Parabolic Partial Differential Equations; Nonsmooth Initial Data; Error Estimates



Denna post skapades 2015-01-09. Senast ändrad 2015-02-16.
CPL Pubid: 210370

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Numerisk analys

Chalmers infrastruktur