Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6916119 | Computer Methods in Applied Mechanics and Engineering | 2016 | 21 Pages |
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 kâ¥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.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science Applications
Authors
Daniele A. Di Pietro, Alexandre Ern, Alexander Linke, Friedhelm Schieweck,