# Cell centered Galerkin methods for diffusive problems

ESAIM: Mathematical Modelling and Numerical Analysis (2011)

- Volume: 46, Issue: 1, page 111-144
- ISSN: 0764-583X

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topDi Pietro, Daniele A.. "Cell centered Galerkin methods for diffusive problems." ESAIM: Mathematical Modelling and Numerical Analysis 46.1 (2011): 111-144. <http://eudml.org/doc/222101>.

@article{DiPietro2011,

abstract = {
In this work we introduce a new class of lowest order methods for
diffusive problems on general meshes with only one unknown per
element.
The underlying idea is to construct an incomplete piecewise affine
polynomial space with optimal approximation properties starting
from values at cell centers.
To do so we borrow ideas from multi-point finite volume methods,
although we use them in a rather different context.
The incomplete polynomial space replaces classical complete
polynomial spaces in discrete formulations inspired by discontinuous
Galerkin methods.
Two problems are studied in this work:
a heterogeneous anisotropic diffusion problem, which is used
to lay the pillars of the method, and the incompressible
Navier-Stokes equations, which provide a more realistic
application.
An exhaustive theoretical study as well as a set of numerical
examples featuring different difficulties are provided.
},

author = {Di Pietro, Daniele A.},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Cell centered Galerkin; finite volumes; discontinuous
Galerkin; heterogeneous anisotropic diffusion; incompressible
Navier-Stokes equations; cell centered Galerkin method; discontinuous Galerkin method; incompressible Navier-Stokes equations; numerical examples; finite element; convergence},

language = {eng},

month = {8},

number = {1},

pages = {111-144},

publisher = {EDP Sciences},

title = {Cell centered Galerkin methods for diffusive problems},

url = {http://eudml.org/doc/222101},

volume = {46},

year = {2011},

}

TY - JOUR

AU - Di Pietro, Daniele A.

TI - Cell centered Galerkin methods for diffusive problems

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2011/8//

PB - EDP Sciences

VL - 46

IS - 1

SP - 111

EP - 144

AB -
In this work we introduce a new class of lowest order methods for
diffusive problems on general meshes with only one unknown per
element.
The underlying idea is to construct an incomplete piecewise affine
polynomial space with optimal approximation properties starting
from values at cell centers.
To do so we borrow ideas from multi-point finite volume methods,
although we use them in a rather different context.
The incomplete polynomial space replaces classical complete
polynomial spaces in discrete formulations inspired by discontinuous
Galerkin methods.
Two problems are studied in this work:
a heterogeneous anisotropic diffusion problem, which is used
to lay the pillars of the method, and the incompressible
Navier-Stokes equations, which provide a more realistic
application.
An exhaustive theoretical study as well as a set of numerical
examples featuring different difficulties are provided.

LA - eng

KW - Cell centered Galerkin; finite volumes; discontinuous
Galerkin; heterogeneous anisotropic diffusion; incompressible
Navier-Stokes equations; cell centered Galerkin method; discontinuous Galerkin method; incompressible Navier-Stokes equations; numerical examples; finite element; convergence

UR - http://eudml.org/doc/222101

ER -

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