# Cell centered Galerkin methods for diffusive problems

- 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 - Modélisation Mathématique et Analyse Numérique 46.1 (2012): 111-144. <http://eudml.org/doc/273335>.

@article{DiPietro2012,

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 - Modélisation Mathématique et Analyse Numérique},

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

language = {eng},

number = {1},

pages = {111-144},

publisher = {EDP-Sciences},

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

url = {http://eudml.org/doc/273335},

volume = {46},

year = {2012},

}

TY - JOUR

AU - Di Pietro, Daniele A.

TI - Cell centered Galerkin methods for diffusive problems

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2012

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; numerical examples; finite element; convergence

UR - http://eudml.org/doc/273335

ER -

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