Flux-Upwind Stabilization of the Discontinuous Petrov-Galerkin Formulation with Lagrangian Multipliers for Advection-Diffusion Problems
Articolo
Data di Pubblicazione:
2005
Citazione:
Flux-Upwind Stabilization of the Discontinuous Petrov-Galerkin Formulation
with Lagrangian Multipliers for Advection-Diffusion Problems / P.Causin, R. Sacco, C. Bottasso. - In: MODÉLISATION MATHÉMATIQUE ET ANALYSE NUMÉRIQUE. - ISSN 0764-583X. - 39:6(2005), pp. 1087-1114.
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 $H^1$-norm, and the numerical performance
of the scheme is validated on benchmark problems with
sharp internal and boundary layers.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Advection-diffusion problems; Discontinuous Galerkin and Petrov-Galerkin methods; Finite element methods; Mixed and hybrid methods; Nonconforming finite elements; Stabilized finite elements; Upwinding
Elenco autori:
P.Causin, R. Sacco, C. Bottasso
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