New mixed finite volume methods for second order eliptic problems

Kwang Y. Kim

ESAIM: Mathematical Modelling and Numerical Analysis (2006)

  • Volume: 40, Issue: 1, page 123-147
  • ISSN: 0764-583X

Abstract

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In this paper we introduce and analyze new mixed finite volume methods for second order elliptic problems which are based on H(div)-conforming approximations for the vector variable and discontinuous approximations for the scalar variable. The discretization is fulfilled by combining the ideas of the traditional finite volume box method and the local discontinuous Galerkin method. We propose two different types of methods, called Methods I and II, and show that they have distinct advantages over the mixed methods used previously. In particular, a clever elimination of the vector variable leads to a primal formulation for the scalar variable which closely resembles discontinuous finite element methods. We establish error estimates for these methods that are optimal for the scalar variable in both methods and for the vector variable in Method II.

How to cite

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Kim, Kwang Y.. "New mixed finite volume methods for second order eliptic problems." ESAIM: Mathematical Modelling and Numerical Analysis 40.1 (2006): 123-147. <http://eudml.org/doc/249758>.

@article{Kim2006,
abstract = { In this paper we introduce and analyze new mixed finite volume methods for second order elliptic problems which are based on H(div)-conforming approximations for the vector variable and discontinuous approximations for the scalar variable. The discretization is fulfilled by combining the ideas of the traditional finite volume box method and the local discontinuous Galerkin method. We propose two different types of methods, called Methods I and II, and show that they have distinct advantages over the mixed methods used previously. In particular, a clever elimination of the vector variable leads to a primal formulation for the scalar variable which closely resembles discontinuous finite element methods. We establish error estimates for these methods that are optimal for the scalar variable in both methods and for the vector variable in Method II. },
author = {Kim, Kwang Y.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Mixed method; finite volume method; discontinuous finite element method; conservative method.; conservative method; mixed finite volume methods; local discontinuous Galerkin method; mixed finite element methods; error estimates},
language = {eng},
month = {2},
number = {1},
pages = {123-147},
publisher = {EDP Sciences},
title = {New mixed finite volume methods for second order eliptic problems},
url = {http://eudml.org/doc/249758},
volume = {40},
year = {2006},
}

TY - JOUR
AU - Kim, Kwang Y.
TI - New mixed finite volume methods for second order eliptic problems
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2006/2//
PB - EDP Sciences
VL - 40
IS - 1
SP - 123
EP - 147
AB - In this paper we introduce and analyze new mixed finite volume methods for second order elliptic problems which are based on H(div)-conforming approximations for the vector variable and discontinuous approximations for the scalar variable. The discretization is fulfilled by combining the ideas of the traditional finite volume box method and the local discontinuous Galerkin method. We propose two different types of methods, called Methods I and II, and show that they have distinct advantages over the mixed methods used previously. In particular, a clever elimination of the vector variable leads to a primal formulation for the scalar variable which closely resembles discontinuous finite element methods. We establish error estimates for these methods that are optimal for the scalar variable in both methods and for the vector variable in Method II.
LA - eng
KW - Mixed method; finite volume method; discontinuous finite element method; conservative method.; conservative method; mixed finite volume methods; local discontinuous Galerkin method; mixed finite element methods; error estimates
UR - http://eudml.org/doc/249758
ER -

References

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