On Conforming Finite Element Methods for the Inhomogeneous Stationary Navier-Stokes Equations.
On discontinuous Galerkin method and semiregular family of triangulations
Discretization of second order elliptic partial differential equations by discontinuous Galerkin method often results in numerical schemes with penalties. In this paper we analyze these penalized schemes in the context of quite general triangular meshes satisfying only a semiregularity assumption. A new (modified) penalty term is presented and theoretical properties are proven together with illustrative numerical results.
On equilibrium finite elements in three-dimensional case
The space of divergence-free functions with vanishing normal flux on the boundary is approximated by subspaces of finite elements that have the same property. The easiest way of generating basis functions in these subspaces is considered.
On exact results in the finite element method
We prove that the finite element method for one-dimensional problems yields no discretization error at nodal points provided the shape functions are appropriately chosen. Then we consider a biharmonic problem with mixed boundary conditions and the weak solution . We show that the Galerkin approximation of based on the so-called biharmonic finite elements is independent of the values of in the interior of any subelement.
On FE-grid relocation in solving unilateral boundary value problems by FEM
We consider FE-grid optimization in elliptic unilateral boundary value problems. The criterion used in grid optimization is the total potential energy of the system. It is shown that minimization of this cost functional means a decrease of the discretization error or a better approximation of the unilateral boundary conditions. Design sensitivity analysis is given with respect to the movement of nodal points. Numerical results for the Dirichlet-Signorini problem for the Laplace equation and the...
On Finite Element Approximation of the Gradient for Solution of Poisson Equation.
On Finite Element Approximations to Time-Dependent Problems.
On Finite Element Methods for 2nd order (semi–) periodic Eigenvalue Problems
We deal with a class of elliptic eigenvalue problems (EVPs) on a rectangle Ω ⊂ R^2 , with periodic or semi–periodic boundary conditions (BCs) on ∂Ω. First, for both types of EVPs, we pass to a proper variational formulation which is shown to fit into the general framework of abstract EVPs for symmetric, bounded, strongly coercive bilinear forms in Hilbert spaces, see, e.g., [13, §6.2]. Next, we consider finite element methods (FEMs) without and with numerical quadrature. The aim of the paper is...
On Finite Element Methods for Plasticity Problems.
On Finite Element Methods for the Neumann Problem.
On Galerkin approximations of parabolic equations in time dependent domains
On internal approximations of parabolic problems
On interpolation error on degenerating prismatic elements
We propose an analogue of the maximum angle condition (commonly used in finite element analysis for triangular and tetrahedral meshes) for the case of prismatic elements. Under this condition, prisms in the meshes may degenerate in certain ways, violating the so-called inscribed ball condition presented by P. G. Ciarlet (1978), but the interpolation error remains of the order in the -norm for sufficiently smooth functions.
On iterative solution of nonlinear heat-conduction and diffusion problems
The present paper deals with the numerical solution of the nonlinear heat equation. An iterative method is suggested in which the iterations are obtained by solving linear heat equation. The convergence of the method is proved under very natural conditions on given input data of the original problem. Further, questions of convergence of the Galerkin method applied to the original equation as well as to the linear equations in the above mentioned iterative method are studied.
On Lagrange and Hermite Interpolation in Rk.
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.