Flux-Upwind Stabilization of the Discontinuous Petrov-Galerkin Formulation with Lagrange Multipliers for Advection-Diffusion Problems

MOX 34

Flux-Upwind Stabilization of the Discontinuous Petrov-Galerkin Formulation with Lagrange Multipliers for Advection-Diffusion Problems

Tuesday 30th March 2004

Bottasso, Carlo L.; Causin, Paola; Sacco, Riccardo

In this work we considerthe 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 $H^1-norm$, anf the numerical performance of the scheme is validated on benchmark problems with sharp internal and boundary layers.