An advection-robust Hybrid High-Order method for the Oseen problem

Abstract : In this work, we study advection-robust Hybrid High-Order discretizations of the Oseen equations. For a given integer $k\ge 0$, the discrete velocity unknowns are vector-valued polynomials of total degree $\le k$ on mesh elements and faces, while the pressure unknowns are discontinuous polynomials of total degree $\le k$ on the mesh. From the discrete unknowns, three relevant quantities are reconstructed inside each element: a velocity of total degree $\le(k+1)$, 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 $h_T$ contributes to the discretization error with an $\mathcal{O}(h_T^{k+1})$-term in the diffusion-dominated regime, an $\mathcal{O}(h_T^{k+\frac12})$-term in the advection-dominated regime, and scales with intermediate powers of $h_T$ in between. Numerical results complete the exposition.
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Journal of Scientific Computing, Springer Verlag, 2018, 77 (3), pp.1310-1338
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Dernière modification le : dimanche 16 décembre 2018 - 14:21:47

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  • HAL Id : hal-01658263, version 2

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Joubine Aghili, Daniele Antonio Di Pietro. An advection-robust Hybrid High-Order method for the Oseen problem. Journal of Scientific Computing, Springer Verlag, 2018, 77 (3), pp.1310-1338. 〈hal-01658263v2〉

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