WIAS Preprint No. 2195, (2015)

A discontinuous skeletal method for the viscosity-dependent Stokes problem



Authors

  • Ern, Alexandre
  • di Pietro, Daniele
  • Linke, Alexander
    ORCID: 0000-0002-0165-2698
  • Schieweck, Friedhelm

2010 Mathematics Subject Classification

  • 65N12 65N30 76D07

2008 Physics and Astronomy Classification Scheme

  • 47.11.Fg

Keywords

  • Stokes problem, mixed methods, curl-free forces, higher-order reconstruction, superconvergence, hybrid discontinuous Galerkin method, static condensation

Abstract

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 >=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 L2-pressure estimate of order (k+1) and an L2-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.

Appeared in

  • Comput. Methods Appl. Mech. Engrg., 306 (2016) pp. 175--195.

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