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262
We present the convergence analysis of an efficient numerical method for the solution of an initial-boundary value problem for a scalar nonlinear conservation law equation with a diffusion term. Nonlinear convective terms are approximated with the aid of a monotone finite volume scheme considered over the finite volume barycentric mesh, whereas the diffusion term is discretized by piecewise linear nonconforming triangular finite elements. Under the assumption that the triangulations are of weakly...
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...
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...
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...
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.
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...
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...
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,...
The aim of this paper is to give a simple, introductory presentation of the extension of the Virtual Element Method to the discretization of H(div)-conforming vector fields (or, more generally, of (n − 1) − Cochains). As we shall see, the methods presented here can be seen as extensions of the so-called BDM family to deal with more general element geometries (such as polygons with an almost arbitrary geometry). For the sake of simplicity, we limit ourselves to the 2-dimensional case, with the aim...
The dynamical investigation of two-component poroelastic media is important for practical applications. Analytic solution methods are often not available since they are too complicated for the complex governing sets of equations. For this reason, often some existing numerical methods are used. In this work results obtained with the finite element method are opposed to those obtained by Schanz using the boundary element method. Not only the influence of the number of elements and time steps on the...
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262