Superconvergence and Asymptotic Expansions for Bilinear Finite Volume Element Approximations

Superconvergence and Asymptotic Expansions for Bilinear Finite Volume Element Approximations

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.

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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.

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