# New mixed finite volume methods for second order eliptic problems

ESAIM: Mathematical Modelling and Numerical Analysis (2006)

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

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topKim, 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 -

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