Analysis of the hydrostatic approximation in oceanography with compression term
Analysis of the hydrostatic approximation in oceanography with compression term
Analysis of the hydrostatic approximation in oceanography with compression term
The hydrostatic approximation of the incompressible 3D stationary Navier-Stokes equations is widely used in oceanography and other applied sciences. It appears through a limit process due to the anisotropy of the domain in use, an ocean, and it is usually studied as such. We consider in this paper an equivalent formulation to this hydrostatic approximation that includes Coriolis force and an additional pressure term that comes from taking into account the pressure in the state equation for...
Analysis of the hydrostatic approximation in oceanography with compression term
The hydrostatic approximation of the incompressible 3D stationary Navier-Stokes equations is widely used in oceanography and other applied sciences. It appears through a limit process due to the anisotropy of the domain in use, an ocean, and it is usually studied as such. We consider in this paper an equivalent formulation to this hydrostatic approximation that includes Coriolis force and an additional pressure term that comes from taking into account the pressure in the state equation for...
Anisotropic mesh adaption: application to computational fluid dynamics
In this communication we focus on goal-oriented anisotropic adaption techniques. Starting point has been the derivation of suitable anisotropic interpolation error estimates for piecewise linear finite elements, on triangular grids in . Then we have merged these interpolation estimates with the dual-based a posteriori error analysis proposed by R. Rannacher and R. Becker. As examples of this general anisotropic a posteriori analysis, elliptic, advection-diffusion-reaction and the Stokes problems...
Approximation and eigenvalue extrapolation of Stokes eigenvalue problem by nonconforming finite element methods
In this paper we analyze the stream function-vorticity-pressure method for the Stokes eigenvalue problem. Further, we obtain full order convergence rate of the eigenvalue approximations for the Stokes eigenvalue problem based on asymptotic error expansions for two nonconforming finite elements, and . Using the technique of eigenvalue error expansion, the technique of integral identities and the extrapolation method, we can improve the accuracy of the eigenvalue approximations.
Approximation by finite element method of the model plasma problem
Approximation of a nonlinear elliptic problem arising in a non-newtonian fluid flow model in glaciology
The main goal of this article is to establish a priori and a posteriori error estimates for the numerical approximation of some non linear elliptic problems arising in glaciology. The stationary motion of a glacier is given by a non-newtonian fluid flow model which becomes, in a first two-dimensional approximation, the so-called infinite parallel sided slab model. The approximation of this model is made by a finite element method with piecewise polynomial functions of degree 1. Numerical results...
Approximation of a nonlinear elliptic problem arising in a non-Newtonian fluid flow model in glaciology
The main goal of this article is to establish a priori and a posteriori error estimates for the numerical approximation of some non linear elliptic problems arising in glaciology. The stationary motion of a glacier is given by a non-Newtonian fluid flow model which becomes, in a first two-dimensional approximation, the so-called infinite parallel sided slab model. The approximation of this model is made by a finite element method with piecewise polynomial functions of degree 1. Numerical results...
Approximation of an eigenvalue problem associated with the Stokes problem by the stream function-vorticity-pressure method
By means of eigenvalue error expansion and integral expansion techniques, we propose and analyze the stream function-vorticity-pressure method for the eigenvalue problem associated with the Stokes equations on the unit square. We obtain an optimal order of convergence for eigenvalues and eigenfuctions. Furthermore, for the bilinear finite element space, we derive asymptotic expansions of the eigenvalue error, an efficient extrapolation and an a posteriori error estimate for the eigenvalue. Finally,...
Approximation of the three-field Stokes system via optimized quadrilateral finite elements
Atmospheric reentry dynamics of conic objects.