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 -norm, and the numerical performance of the scheme is validated on benchmark problems with sharp internal and boundary layers.
Mots-clés : finite element methods, mixed and hybrid methods, discontinuous Galerkin and Petrov-Galerkin methods, nonconforming finite elements, stabilized finite elements, upwinding, advection-diffusion problems
@article{M2AN_2005__39_6_1087_0,
author = {Causin, Paola and Sacco, Riccardo and Bottasso, Carlo L.},
title = {Flux-upwind stabilization of the discontinuous {Petrov-Galerkin} formulation with {Lagrange} multipliers for advection-diffusion problems},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {1087--1114},
publisher = {EDP-Sciences},
volume = {39},
number = {6},
year = {2005},
doi = {10.1051/m2an:2005050},
zbl = {1084.65105},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2005050/}
}
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: Modélisation mathématique et analyse numérique PY - 2005 SP - 1087 EP - 1114 VL - 39 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2005050/ DO - 10.1051/m2an:2005050 LA - en ID - M2AN_2005__39_6_1087_0 ER -
%0 Journal Article %A Causin, Paola %A Sacco, Riccardo %A Bottasso, Carlo L. %T Flux-upwind stabilization of the discontinuous Petrov-Galerkin formulation with Lagrange multipliers for advection-diffusion problems %J ESAIM: Modélisation mathématique et analyse numérique %D 2005 %P 1087-1114 %V 39 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2005050/ %R 10.1051/m2an:2005050 %G en %F M2AN_2005__39_6_1087_0
Causin, Paola; Sacco, Riccardo; Bottasso, Carlo L. Flux-upwind stabilization of the discontinuous Petrov-Galerkin formulation with Lagrange multipliers for advection-diffusion problems. ESAIM: Modélisation mathématique et analyse numérique, Tome 39 (2005) no. 6, pp. 1087-1114. doi : 10.1051/m2an:2005050. http://www.numdam.org/articles/10.1051/m2an:2005050/
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