# Flux-upwind stabilization of the discontinuous Petrov–Galerkin formulation with Lagrange multipliers for advection-diffusion problems

Paola Causin; Riccardo Sacco; Carlo L. Bottasso

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 39, Issue: 6, page 1087-1114
- ISSN: 0764-583X

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topCausin, Paola, Sacco, Riccardo, and Bottasso, Carlo L.. "Flux-upwind stabilization of the discontinuous Petrov–Galerkin formulation with Lagrange multipliers for advection-diffusion problems." ESAIM: Mathematical Modelling and Numerical Analysis 39.6 (2010): 1087-1114. <http://eudml.org/doc/194298>.

@article{Causin2010,

abstract = {
In this work we consider the
dual-primal Discontinuous Petrov–Galerkin (DPG)
method for the advection-diffusion model problem.
Since in the DPG method both
mixed internal variables are discontinuous,
a static condensation procedure can be
carried out, leading to a single-field nonconforming
discretization scheme. For this latter formulation,
we propose a flux-upwind stabilization technique to deal with
the advection-dominated case.
The resulting scheme is conservative and satisfies a discrete
maximum principle under standard geometrical assumptions on
the computational grid. A convergence analysis is
developed, proving first-order accuracy of the
method in a discrete H1-norm, and the numerical performance
of the scheme is validated on benchmark problems with
sharp internal and boundary layers.
},

author = {Causin, Paola, Sacco, Riccardo, Bottasso, Carlo L.},

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

keywords = {Finite element methods; mixed and hybrid methods;
discontinuous Galerkin and Petrov–Galerkin methods;
nonconforming finite elements;
stabilized finite elements; upwinding;
advection-diffusion problems.; finite element methods; numerical examples; convergence; discontinuous Galerkin and Petrov-Galerkin methods; nonconforming finite elements; stabilized finite elements; advection-diffusion problems},

language = {eng},

month = {3},

number = {6},

pages = {1087-1114},

publisher = {EDP Sciences},

title = {Flux-upwind stabilization of the discontinuous Petrov–Galerkin formulation with Lagrange multipliers for advection-diffusion problems},

url = {http://eudml.org/doc/194298},

volume = {39},

year = {2010},

}

TY - JOUR

AU - Causin, Paola

AU - Sacco, Riccardo

AU - Bottasso, Carlo L.

TI - Flux-upwind stabilization of the discontinuous Petrov–Galerkin formulation with Lagrange multipliers for advection-diffusion problems

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 39

IS - 6

SP - 1087

EP - 1114

AB -
In this work we consider the
dual-primal Discontinuous Petrov–Galerkin (DPG)
method for the advection-diffusion model problem.
Since in the DPG method both
mixed internal variables are discontinuous,
a static condensation procedure can be
carried out, leading to a single-field nonconforming
discretization scheme. For this latter formulation,
we propose a flux-upwind stabilization technique to deal with
the advection-dominated case.
The resulting scheme is conservative and satisfies a discrete
maximum principle under standard geometrical assumptions on
the computational grid. A convergence analysis is
developed, proving first-order accuracy of the
method in a discrete H1-norm, and the numerical performance
of the scheme is validated on benchmark problems with
sharp internal and boundary layers.

LA - eng

KW - Finite element methods; mixed and hybrid methods;
discontinuous Galerkin and Petrov–Galerkin methods;
nonconforming finite elements;
stabilized finite elements; upwinding;
advection-diffusion problems.; finite element methods; numerical examples; convergence; discontinuous Galerkin and Petrov-Galerkin methods; nonconforming finite elements; stabilized finite elements; advection-diffusion problems

UR - http://eudml.org/doc/194298

ER -

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