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- Title
A new DG method for a pure–stress formulation of the Brinkman problem with strong symmetry.
- Authors
Meddahi, Salim; Ruiz-Baier, Ricardo
- 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.
- Subjects
GALERKIN methods; STRAINS &; stresses (Mechanics); SYMMETRY; VELOCITY
- Publication
Networks & Heterogeneous Media, 2022, Vol 17, Issue 6, p1
- ISSN
1556-1801
- Publication type
Article
- DOI
10.3934/nhm.2022031