Asymptotic Theory of the Global Error and Some Techniques of Error Estimation.
Automatic simplification of Darcy’s equations with pressure dependent permeability
We consider the flow of a viscous incompressible fluid in a rigid homogeneous porous medium provided with mixed boundary conditions. Since the boundary pressure can present high variations, the permeability of the medium also depends on the pressure, so that the model is nonlinear. A posteriori estimates allow us to omit this dependence where the pressure does not vary too much. We perform the numerical analysis of a spectral element discretization of the simplified model. Finally we propose a strategy...
Averaging of gradient in the space of linear triangular and bilinear rectangular finite elements
An averaging method for the second-order approximation of the values of the gradient of an arbitrary smooth function u = u(x 1, x 2) at the vertices of a regular triangulation T h composed both of rectangles and triangles is presented. The method assumes that only the interpolant Πh[u] of u in the finite element space of the linear triangular and bilinear rectangular finite elements from T h is known. A complete analysis of this method is an extension of the complete analysis concerning the finite...
Axissymmetric Free Surface Seepage
Aппроксимация обобщенных решений с помощью конечных разностей
Basic compactness properties of nonconforming and hybrid finite element spaces
Basic principles of mixed Virtual Element Methods
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...
Behavior of plane relaxation methods as multigrid smoothers.
Behavior of the error of the approximate solutions of boundary value problems for linear elliptic operators by Galerkin's and finite difference methods
Besov Regularity for Second Order Elliptic Boundary Value Problems with Variable Coefficients.
Beziehungen zwischen den Verfahren von Ritz und Bazley
Boundary augmented Lagrangian method for the Signorini problem
An augmented Lagrangian method, based on boundary variational formulations and fixed point method, is designed and analyzed for the Signorini problem of the Laplacian. Using the equivalence between Signorini boundary conditions and a fixed-point problem, we develop a new iterative algorithm that formulates the Signorini problem as a sequence of corresponding variational equations with the Steklov-Poincaré operator. Both theoretical results and numerical experiments show that the method presented...
Boundary controllability of the finite-difference space semi-discretizations of the beam equation
We propose a finite difference semi-discrete scheme for the approximation of the boundary exact controllability problem of the 1-D beam equation modelling the transversal vibrations of a beam with fixed ends. First of all we show that, due to the high frequency spurious oscillations, the uniform (with respect to the mesh-size) controllability property of the semi-discrete model fails in the natural functional setting. We then prove that there are two ways of restoring the uniform controllability...
Boundary controllability of the finite-difference space semi-discretizations of the beam equation
We propose a finite difference semi-discrete scheme for the approximation of the boundary exact controllability problem of the 1-D beam equation modelling the transversal vibrations of a beam with fixed ends. First of all we show that, due to the high frequency spurious oscillations, the uniform (with respect to the mesh-size) controllability property of the semi-discrete model fails in the natural functional setting. We then prove that there are two ways of restoring the uniform controllability...
Boundary integral equations for mixed boundary value problems in polygonal domains and Galerkin approximation
Boundary Lagrange multipliers in finite element methods: error analysis in natural forms.
Boundary Subspaces for the Finite Element Method With Lagrange Multipliers.
Brève communication. Utilisation en analyse numérique de la formule de variation d'Hadamard
Cache optimization for structured and unstructured grid multigrid.
Calcul des courants induits et des forces électromagnétiques dans un système de conducteurs mobiles