2017/12/07 by Aghili, Joubine, Di Pietro, Daniele A. · 1 citation
#65N08 #65N12 #65N30 #76D07 #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.1712.02625
In this work, we study advection-robust Hybrid High-Order discretizations of the Oseen equations. For a given integer k≥ 0, the discrete velocity unknowns are vector-valued polynomials of total degree ≤ k on mesh elements and faces, while the pressure unknowns are discontinuous polynomials of total degree ≤ k on the mesh. From the discrete unknowns, three relevant quantities are reconstructed inside each element: a velocity of total degree ≤(k+1), a discrete advective derivative, and a discrete divergence. These reconstructions are used to formulate the discretizations of the viscous, advective, and velocity-pressure coupling terms, respectively. Well-posedness is ensured through appropriate high-order stabilization terms. We prove energy error estimates that are advection-robust for the velocity, and show that each mesh element T of diameter hT contributes to the discretization error with an O(hTk+1)-term in the diffusion-dominated regime, an O(hTk+\frac12)-term in the advection-dominated regime, and scales with intermediate powers of hT in between. Numerical results complete the exposition.