RT journal article
T1 Numerical analysis of a stable discontinuous Galerkin scheme for the hydrostatic Stokes problem
A1 Guillén González, Francisco
A1 Redondo Neble, María Victoria
A1 Rodríguez Galván, José Rafael
A2 Matemáticas
K1 discontinuous Galerkin; hydrostatic Stokes; numerical analysis; stability
AB 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 𝓟�2/𝓟�1 or bubble 𝓟�1b/𝓟�1. Here we prove stability for our 𝓟�k/𝓟�k DG scheme. Some novel numerical tests are provided which are in agreement with the previous analysis.
PB De Gruyter Open Ltd
SN 1570-2820
YR 2021
FD 2021-07-03
LK http://hdl.handle.net/10498/30875
UL http://hdl.handle.net/10498/30875
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 08-nov-2026