TY - JOUR
T1 - Some error estimates for the finite volume element method for a parabolic problem
AU - Chatzipantelidis, Panagiotis
AU - Lazarov, Raytcho
AU - Thomée, Vidar
N1 - KAUST Repository Item: Exported on 2021-07-02
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: The research of R. D. Lazarov was supported in parts by US NSF Grant DMS-1016525 and by award KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). The research of P. Chatzipantelidis was partly supported by the FP7-REGPOT-2009-1 project “Archimedes Center for Modeling Analysis and Computation”, funded by the European Commission.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
PY - 2013/7/1
Y1 - 2013/7/1
N2 - 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), 1-20] 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. © 2013 Institute of Mathematics.
AB - 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), 1-20] 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. © 2013 Institute of Mathematics.
UR - http://hdl.handle.net/10754/669881
UR - https://www.degruyter.com/document/doi/10.1515/cmam-2012-0006/html
UR - http://www.scopus.com/inward/record.url?scp=84881590565&partnerID=8YFLogxK
U2 - 10.1515/cmam-2012-0006
DO - 10.1515/cmam-2012-0006
M3 - Article
SN - 1609-4840
VL - 13
SP - 251
EP - 279
JO - Computational Methods in Applied Mathematics
JF - Computational Methods in Applied Mathematics
IS - 3
ER -