A second-order finite volume element method on quadrilateral meshes for elliptic equations

Min Yang

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2006)

  • Volume: 40, Issue: 6, page 1053-1067
  • ISSN: 0764-583X

Abstract

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In this paper, by use of affine biquadratic elements, we construct and analyze a finite volume element scheme for elliptic equations on quadrilateral meshes. The scheme is shown to be of second-order in H 1 -norm, provided that each quadrilateral in partition is almost a parallelogram. Numerical experiments are presented to confirm the usefulness and efficiency of the method.

How to cite

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Yang, Min. "A second-order finite volume element method on quadrilateral meshes for elliptic equations." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 40.6 (2006): 1053-1067. <http://eudml.org/doc/245235>.

@article{Yang2006,
abstract = {In this paper, by use of affine biquadratic elements, we construct and analyze a finite volume element scheme for elliptic equations on quadrilateral meshes. The scheme is shown to be of second-order in $H^1$-norm, provided that each quadrilateral in partition is almost a parallelogram. Numerical experiments are presented to confirm the usefulness and efficiency of the method.},
author = {Yang, Min},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {finite volume element; second-order; quadrilateral meshes; error estimates; mixed finite element finite volume method; elliptic problem; convergence; a priori error estimates},
language = {eng},
number = {6},
pages = {1053-1067},
publisher = {EDP-Sciences},
title = {A second-order finite volume element method on quadrilateral meshes for elliptic equations},
url = {http://eudml.org/doc/245235},
volume = {40},
year = {2006},
}

TY - JOUR
AU - Yang, Min
TI - A second-order finite volume element method on quadrilateral meshes for elliptic equations
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2006
PB - EDP-Sciences
VL - 40
IS - 6
SP - 1053
EP - 1067
AB - In this paper, by use of affine biquadratic elements, we construct and analyze a finite volume element scheme for elliptic equations on quadrilateral meshes. The scheme is shown to be of second-order in $H^1$-norm, provided that each quadrilateral in partition is almost a parallelogram. Numerical experiments are presented to confirm the usefulness and efficiency of the method.
LA - eng
KW - finite volume element; second-order; quadrilateral meshes; error estimates; mixed finite element finite volume method; elliptic problem; convergence; a priori error estimates
UR - http://eudml.org/doc/245235
ER -

References

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