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

Min Yang

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

  • 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 H1-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 40.6 (2007): 1053-1067. <http://eudml.org/doc/194344>.

@article{Yang2007,
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 H1-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},
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},
month = {2},
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/194344},
volume = {40},
year = {2007},
}

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
DA - 2007/2//
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 H1-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/194344
ER -

References

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