Flux-upwind stabilization of the discontinuous Petrov–Galerkin formulation with Lagrange multipliers for advection-diffusion problems
INRIA Rocquencourt, Domaine de Voluceau,
Rocquencourt BP 105, 78153 Le Chesnay Cedex, France
2 Dipartimento di Matematica “F. Brioschi”, Politecnico di Milano, via Bonardi 9, 20133 Milano, Italy. email@example.com
3 D. Guggenheim School of Aerospace Engineering, Georgia Institute of Technology, 270 Ferst Dr., 30332 Atlanta GA, USA
Revised: 10 March 2005
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.
Mathematics Subject Classification: 65N99
Key words: Finite element methods / mixed and hybrid methods / discontinuous Galerkin and Petrov–Galerkin methods / nonconforming finite elements / stabilized finite elements / upwinding / advection-diffusion problems.
© EDP Sciences, SMAI, 2005