On Some High Accuracy Difference Schemes for Solving Elliptic Equations.
On some implicit and semi-implicit staggered schemes for the shallow water and Euler equations
In this paper, we propose implicit and semi-implicit in time finite volume schemes for the barotropic Euler equations (hence, as a particular case, for the shallow water equations) and for the full Euler equations, based on staggered discretizations. For structured meshes, we use the MAC finite volume scheme, and, for general mixed quadrangular/hexahedral and simplicial meshes, we use the discrete unknowns of the Rannacher−Turek or Crouzeix−Raviart finite elements. We first show that a solution...
On some nonlinear potential problems.
On spectral approximation. Part 1. The problem of convergence
On spectral approximation. Part 2. Error estimates for the Galerkin method
On stability of the element for incompressible flow problems
It is well known that finite element spaces used for approximating the velocity and the pressure in an incompressible flow problem have to be stable in the sense of the inf-sup condition of Babuška and Brezzi if a stabilization of the incompressibility constraint is not applied. In this paper we consider a recently introduced class of triangular nonconforming finite elements of th order accuracy in the energy norm called elements. For we show that the stability condition holds if the velocity...
On step approximation for Roseau's analytical solution of water waves.
On suitable inlet boundary conditions for fluid-structure interaction problems in a channel
We are interested in the numerical solution of a two-dimensional fluid-structure interaction problem. A special attention is paid to the choice of physically relevant inlet boundary conditions for the case of channel closing. Three types of the inlet boundary conditions are considered. Beside the classical Dirichlet and the do-nothing boundary conditions also a generalized boundary condition motivated by the penalization prescription of the Dirichlet boundary condition is applied. The fluid flow...
On Synge-type angle condition for -simplices
The maximum angle condition of J. L. Synge was originally introduced in interpolation theory and further used in finite element analysis and applications for triangular and later also for tetrahedral finite element meshes. In this paper we present some of its generalizations to higher-dimensional simplicial elements. In particular, we prove optimal interpolation properties of linear simplicial elements in that degenerate in some way.
On the accuracy of multigrid truncation error estimates.
On the application of mixed finite element methods to the wave equations
On the Approximate Solution of Nonlinear Variational Inequalities.
On the approximation of a quasilinear mixed problem
On the approximation of stability factors for general parametrized partial differential equations with a two-level affine decomposition
A new approach for computationally efficient estimation of stability factors for parametric partial differential equations is presented. The general parametric bilinear form of the problem is approximated by two affinely parametrized bilinear forms at different levels of accuracy (after an empirical interpolation procedure). The successive constraint method is applied on the coarse level to obtain a lower bound for the stability factors, and this bound is extended to the fine level by adding a proper...
On the approximation of stability factors for general parametrized partial differential equations with a two-level affine decomposition
A new approach for computationally efficient estimation of stability factors for parametric partial differential equations is presented. The general parametric bilinear form of the problem is approximated by two affinely parametrized bilinear forms at different levels of accuracy (after an empirical interpolation procedure). The successive constraint method is applied on the coarse level to obtain a lower bound for the stability factors, and this...
On the approximation of stability factors for general parametrized partial differential equations with a two-level affine decomposition
A new approach for computationally efficient estimation of stability factors for parametric partial differential equations is presented. The general parametric bilinear form of the problem is approximated by two affinely parametrized bilinear forms at different levels of accuracy (after an empirical interpolation procedure). The successive constraint method is applied on the coarse level to obtain a lower bound for the stability factors, and this...
On the approximation of the exterior Stokes problem in three dimensions
On the approximation of the solution of an optimal control problem governed by an elliptic equation
On the approximation of the spectrum of the Stokes operator
On the Asymptotic Analys of a Non-Symmetric Bar
We study the 3-D elasticity problem in the case of a non-symmetric heterogeneous rod. The asymptotic expansion of the solution is constructed. The coercitivity of the homogenized equation is proved. Estimates are derived for the difference between the truncated series and the exact solution.