On Some Finite Element Procedures for Solving Second Order Boundary Value Problems.
On some nonlinear potential problems.
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 Approximate Solution of Nonlinear Variational Inequalities.
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 asymptotic exactness of Bank-Weiser's estimator.
On the asymptotic exactness of error estimators for linear triangular finite elements.
On the combined effect of boundary approximation and numerical integration on mixed finite element solution of 4th order elliptic problems with variable coefficients
On the combined effect of boundary approximation and numerical integration on mixed finite element solution of 4th order elliptic problems with variable coefficients
Error estimates for the mixed finite element solution of 4th order elliptic problems with variable coefficients, which, in the particular case of aniso-/ortho-/isotropic plate bending problems, gives a direct, simultaneous approximation to bending moment tensor field and displacement field 'u', have been developed considering the combined effect of boundary approximation and numerical integration.
On the Construction of Optimal Mixed Finite Element Methods for the Linear Elasticity Problem.
On the Convergence of a Mixed Finite-Element Method for Plate Bending Problems.
On the convergence of eigenvalues for mixed formulations
On the convergence of gelerkin approximations