On Mixed Finite Element Methods for First Order Elliptic Systems.
On mixed finite element techniques for elliptic problems.
On nonconforming an mixed finite element methods for plate bending problems. The linear case
On nonoverlapping domain decomposition methods for the incompressible Navier-Stokes equations
In this paper, a Dirichlet-Neumann substructuring domain decomposition method is presented for a finite element approximation to the nonlinear Navier-Stokes equations. It is shown that the Dirichlet-Neumann domain decomposition sequence converges geometrically to the true solution provided the Reynolds number is sufficiently small. In this method, subdomain problems are linear. Other version where the subdomain problems are linear Stokes problems is also presented.
On nonoverlapping domain decomposition methods for the incompressible Navier-Stokes equations
In this paper, a Dirichlet-Neumann substructuring domain decomposition method is presented for a finite element approximation to the nonlinear Navier-Stokes equations. It is shown that the Dirichlet-Neumann domain decomposition sequence converges geometrically to the true solution provided the Reynolds number is sufficiently small. In this method, subdomain problems are linear. Other version where the subdomain problems are linear Stokes problems is also presented.
On Numerical Asymptotic Behavior of Finite Element Solutions for Parabolic Equations.
On numerical solution of a variational inequality of the 4th order by finite element method
The problem of a thin elastic plate, deflection of which is limited below by a rigid obstacle is solved. Using Ahlin's and Ari-Adini's elements on rectangles, the convergence is established and SOR method with constraints is proposed for numerical solution.
On numerical solution of weight minimization of elastic bodies weakly supporting tension
Shape optimization of a two-dimensional elastic body is considered, provided the material is weakly supporting tension. The problem generalizes that of a masonry dam subjected to its weight and to the hydrostatic pressure. A part of the boundary has to be found so as to minimize a given cost functional. The numerical realization using a penalty method and finite element technique is presented. Some typical results are shown.
On Patched Variational Principles with Application to Elliptic and Mixed Elliptic-Hyperbolic Problems.
On phase segregation in nonlocal two-particle Hartree systems
We prove the phase segregation phenomenon to occur in the ground state solutions of an interacting system of two self-coupled repulsive Hartree equations for large nonlinear and nonlocal interactions. A self-consistent numerical investigation visualizes the approach to this segregated regime.
On polynomial robustness of flux reconstructions
We deal with the numerical solution of elliptic not necessarily self-adjoint problems. We derive a posteriori upper bound based on the flux reconstruction that can be directly and cheaply evaluated from the original fluxes and we show for one-dimensional problems that local efficiency of the resulting a posteriori error estimators depends on only, where is the discretization polynomial degree. The theoretical results are verified by numerical experiments.
On projection-difference analogues of the identity operator
On semiregular families of triangulations and linear interpolation
We consider triangulations formed by triangular elements. For the standard linear interpolation operator we prove the interpolation order to be for provided the corresponding family of triangulations is only semiregular. In such a case the well-known Zlámal’s condition upon the minimum angle need not be satisfied.
On singularities of capillary surfaces in the absence of gravity.
On solution to an optimal shape design problem in 3-dimensional linear magnetostatics
In this paper we present theoretical, computational, and practical aspects concerning 3-dimensional shape optimization governed by linear magnetostatics. The state solution is approximated by the finite element method using Nédélec elements on tetrahedra. Concerning optimization, the shape controls the interface between the air and the ferromagnetic parts while the whole domain is fixed. We prove the existence of an optimal shape. Then we state a finite element approximation to the optimization...
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...