Year: 2013
Numerical Mathematics: Theory, Methods and Applications, Vol. 6 (2013), Iss. 2 : pp. 408–423
Abstract
Aiming at the isoparametric bilinear finite volume element scheme, we initially derive an asymptotic expansion and a high accuracy combination formula of the derivatives in the sense of pointwise by employing the energy-embedded method on uniform grids. Furthermore, we prove that the approximate derivatives are convergent of order two. Finally, numerical examples verify the theoretical results.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2013.1127nm
Numerical Mathematics: Theory, Methods and Applications, Vol. 6 (2013), Iss. 2 : pp. 408–423
Published online: 2013-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Isoparametric bilinear finite volume element scheme asymptotic expansion high accuracy combination formula superconvergence.
-
Error estimates on a finite volume method for diffusion problems with interface on rectangular grids
Peng, Jie | Shu, Shi | Yu, HaiYuan | Feng, Chunsheng | Kan, Mingxian | Wang, GanghuaApplied Mathematics and Computation, Vol. 311 (2017), Iss. P.335
https://doi.org/10.1016/j.amc.2017.05.029 [Citations: 0] -
Superconvergence and asymptotic expansions for bilinear finite volume element approximation on non-uniform grids
Nie, Cunyun | Shu, Shi | Yu, Haiyuan | Xia, WenhuaJournal of Computational and Applied Mathematics, Vol. 321 (2017), Iss. P.323
https://doi.org/10.1016/j.cam.2016.12.024 [Citations: 4] -
Superconvergence and asymptotic expansion for semidiscrete bilinear finite volume element approximation of the parabolic problem
Nie, Cunyun | Shu, Shi | Yu, Haiyuan | Yang, YuyueComputers & Mathematics with Applications, Vol. 66 (2013), Iss. 1 P.91
https://doi.org/10.1016/j.camwa.2013.02.018 [Citations: 2]