The Discontinuous Petrov-Galerkin Formulation with Lagrange Multipliers for Advection-Diffusion Problems

摘要

We consider the dual-primal Discontinuous Petrov-Galerkin method for the advection-diffusion model problem. A static condensation procedure allows to eliminate the discontinuous internal variables, to obtain a single-field nonconforming discretization scheme. A flux-upwind stabilization technique is then introduced to deal with the advection-dominated case. The resulting scheme is conservative and the stiffness matrix is an M-matrix, which ensures positivity of the solution if the right-hand side is nonnegative. Optimal first-order error estimates are proved for the method in a discrete H~1-novm, and the numerical performance of the scheme is demonstrated on benchmark problems with sharp internal and boundary layers.