@article{Meddahi2022, 
author = {Salim Meddahi and Ricardo Ruiz-Baier},
title = {A new DG method for a pure–stress formulation of the Brinkman problem with strong symmetry},
year = {2022},
journal = {Networks and Heterogeneous Media},
volume = {17},
number = {6},
pages = {893-916},
keywords = {Mixed finite elements, Brinkman problem, discontinuous Galerkin method, parameter-robust error estimates},
url = {https://www.sciopen.com/article/10.3934/nhm.2022031},
doi = {10.3934/nhm.2022031},
abstract = {A strongly symmetric stress approximation is proposed for the Brinkman equations with mixed boundary conditions. The resulting formulation solves for the Cauchy stress using a symmetric interior penalty discontinuous Galerkin method. Pressure and velocity are readily post-processed from stress, and a second post-process is shown to produce exactly divergence-free discrete velocities. We demonstrate the stability of the method with respect to a DG-energy norm and obtain error estimates that are explicit with respect to the coefficients of the problem. We derive optimal rates of convergence for the stress and for the post-processed variables. Moreover, under appropriate assumptions on the mesh, we prove optimal        L    2  -error estimates for the stress. Finally, we provide numerical examples in 2D and 3D.}
}