Finite Volume Methods for Elliptic PDE's: A New Approach

Panagiotis Chatzipantelidis

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 36, Issue: 2, page 307-324
  • ISSN: 0764-583X

Abstract

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We consider a new formulation for finite volume element methods, which is satisfied by known finite volume methods and it can be used to introduce new ones. This framework results by approximating the test function in the formulation of finite element method. We analyze piecewise linear conforming or nonconforming approximations on nonuniform triangulations and prove optimal order H1-norm and L2-norm error estimates.

How to cite

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Chatzipantelidis, Panagiotis. "Finite Volume Methods for Elliptic PDE's: A New Approach." ESAIM: Mathematical Modelling and Numerical Analysis 36.2 (2010): 307-324. <http://eudml.org/doc/194106>.

@article{Chatzipantelidis2010,
abstract = { We consider a new formulation for finite volume element methods, which is satisfied by known finite volume methods and it can be used to introduce new ones. This framework results by approximating the test function in the formulation of finite element method. We analyze piecewise linear conforming or nonconforming approximations on nonuniform triangulations and prove optimal order H1-norm and L2-norm error estimates. },
author = {Chatzipantelidis, Panagiotis},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Finite volume methods; error estimates; finite volume methods; second order elliptic equation; Petrov-Galerkin method; finite elements},
language = {eng},
month = {3},
number = {2},
pages = {307-324},
publisher = {EDP Sciences},
title = {Finite Volume Methods for Elliptic PDE's: A New Approach},
url = {http://eudml.org/doc/194106},
volume = {36},
year = {2010},
}

TY - JOUR
AU - Chatzipantelidis, Panagiotis
TI - Finite Volume Methods for Elliptic PDE's: A New Approach
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 36
IS - 2
SP - 307
EP - 324
AB - We consider a new formulation for finite volume element methods, which is satisfied by known finite volume methods and it can be used to introduce new ones. This framework results by approximating the test function in the formulation of finite element method. We analyze piecewise linear conforming or nonconforming approximations on nonuniform triangulations and prove optimal order H1-norm and L2-norm error estimates.
LA - eng
KW - Finite volume methods; error estimates; finite volume methods; second order elliptic equation; Petrov-Galerkin method; finite elements
UR - http://eudml.org/doc/194106
ER -

References

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