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Pré-Publication, Document De Travail Année : 2015

A discontinuous skeletal method for the viscosity-dependent Stokes problem

Résumé

We devise and analyze arbitrary-order nonconforming methods for the discretization of the viscosity-dependent Stokes equations on simplicial meshes. We keep track explicitly of the viscosity and aim at pressure-robust schemes that can deal with the practically relevant case of body forces with large curl-free part in a way that the discrete velocity error is not spoiled by large pressures. The method is inspired from the recent Hybrid High-Order (HHO) methods for linear elasticity. After elimination of the auxiliary variables by static condensation, the linear system to be solved involves only discrete face-based velocities, which are polynomials of degree $k \ge 0$, and cell-wise constant pressures. Our main result is a pressure-independent energy-error estimate on the velocity of order $(k+1)$. The main ingredient to achieve pressure-independence is the use of a divergence-preserving velocity reconstruction operator in the discretization of the body forces. We also prove an $L^2$-pressure estimate of order $(k+1)$ and an $L^2$-velocity estimate of order $(k+2)$, the latter under elliptic regularity. The local mass and momentum conservation properties of the discretization are also established. Finally, two-and three-dimensional numerical results are presented to support the analysis.
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Dates et versions

hal-01244387 , version 1 (15-12-2015)
hal-01244387 , version 2 (02-05-2016)

Identifiants

  • HAL Id : hal-01244387 , version 1

Citer

Daniele Di Pietro, Alexandre Ern, Alexander Linke, Friedhelm Schieweck. A discontinuous skeletal method for the viscosity-dependent Stokes problem. 2015. ⟨hal-01244387v1⟩
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