Numerical analysis of a stable discontinuous Galerkin scheme for the hydrostatic Stokes problem
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Francisco Guillén-Gonzà lez
Abstract
We propose a Discontinuous Galerkin (DG) scheme for the hydrostatic Stokes equations. These equations, related to large-scale PDE models in oceanography, are characterized by the loss of ellipticity of the vertical momentum equation. This fact provides some interesting challenges, such as the design of stable numerical schemes. The new scheme proposed here is based on the symmetric interior penalty (SIP) technique, with a particular treatment of the vertical velocity. It is well-known that stability of the mixed formulation of primitive equations requires, besides the LBB inf-sup condition, an additional hydrostatic inf-sup restriction relating pressure and vertical velocity. This hydrostatic inf-sup condition invalidates stability of usual Stokes stable continuous finite elements like Taylor-Hood đ2/đ1 or bubble đ1b/đ1. Here we prove stability for our đk/đk DG scheme. Some novel numerical tests are provided which are in agreement with the previous analysis.
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© 2021 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- A finite element method for degenerate two-phase flow in porous media. Part I: Well-posedness
- Numerical analysis of a stable discontinuous Galerkin scheme for the hydrostatic Stokes problem
- Relative error analysis of matrix exponential approximations for numerical integration
- A redistributed bundle algorithm based on local convexification models for nonlinear nonsmooth DC programming
Artikel in diesem Heft
- Frontmatter
- A finite element method for degenerate two-phase flow in porous media. Part I: Well-posedness
- Numerical analysis of a stable discontinuous Galerkin scheme for the hydrostatic Stokes problem
- Relative error analysis of matrix exponential approximations for numerical integration
- A redistributed bundle algorithm based on local convexification models for nonlinear nonsmooth DC programming
