All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 33 Next

Displaying 641 – 660 of 2184

Showing per page

Convergence of a numerical scheme for a nonlinear oblique derivative boundary value problem

Florian Mehats (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We present here a discretization of a nonlinear oblique derivative boundary value problem for the heat equation in dimension two. This finite difference scheme takes advantages of the structure of the boundary condition, which can be reinterpreted as a Burgers equation in the space variables. This enables to obtain an energy estimate and to prove the convergence of the scheme. We also provide some numerical simulations of this problem and a numerical study of the stability of the scheme, which appears...

Convergence of a variational lagrangian scheme for a nonlinear drift diffusion equation

Daniel Matthes, Horst Osberger (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We study a Lagrangian numerical scheme for solution of a nonlinear drift diffusion equation on an interval. The discretization is based on the equation’s gradient flow structure with respect to the Wasserstein distance. The scheme inherits various properties from the continuous flow, like entropy monotonicity, mass preservation, metric contraction and minimum/ maximum principles. As the main result, we give a proof of convergence in the limit of vanishing mesh size under a CFL-type condition. We...

Convergence of an equilibrium finite element model for plane elastostatics

Ivan Hlaváček (1979)

Aplikace matematiky

An equilibrium triangular block-element, proposed by Watwood and Hartz, is subjected to an analysis and its approximability property is proved. If the solution is regular enough, a quasi-optimal error estimate follows for the dual approximation to the mixed boundary value problem of elasticity (based on Castigliano's principle). The convergence is proved even in a general case, when the solution is not regular.

Convergence of Cell Based Finite Volume Discretizations for Problems of Control in the Conduction Coefficients

Anton Evgrafov, Misha Marie Gregersen, Mads Peter Sørensen (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

We present a convergence analysis of a cell-based finite volume (FV) discretization scheme applied to a problem of control in the coefficients of a generalized Laplace equation modelling, for example, a steady state heat conduction. Such problems arise in applications dealing with geometric optimal design, in particular shape and topology optimization, and are most often solved numerically utilizing a finite element approach. Within the FV framework for control in the coefficients problems ...

Convergence of Cell Based Finite Volume Discretizations for Problems of Control in the Conduction Coefficients

Anton Evgrafov, Misha Marie Gregersen, Mads Peter Sørensen (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

We present a convergence analysis of a cell-based finite volume (FV) discretization scheme applied to a problem of control in the coefficients of a generalized Laplace equation modelling, for example, a steady state heat conduction. Such problems arise in applications dealing with geometric optimal design, in particular shape and topology optimization, and are most often solved numerically utilizing a finite element approach. Within the FV framework for control in the coefficients problems ...

Convergence of discretization procedures for problems whose entropy solutions are uniquely characterized by additional relations

Rainer Ansorge (2003)

Applications of Mathematics

Weak solutions of given problems are sometimes not necessarily unique. Relevant solutions are then picked out of the set of weak solutions by so-called entropy conditions. Connections between the original and the numerical entropy condition were often discussed in the particular case of scalar conservation laws, and also a general theory was presented in the literature for general scalar problems. The entropy conditions were realized by certain inequalities not generalizable to systems of equations...

Convergence of dual finite element approximations for unilateral boundary value problems

Ivan Hlaváček (1980)

Aplikace matematiky

A semi-coercive problem with unilateral boundary conditions of the Signoriti type in a convex polygonal domain is solved on the basis of a dual variational approach. Whereas some strong regularity of the solution has been assumed in the previous author’s results on error estimates, no assumption of this kind is imposed here and still the L 2 -convergence is proved.

Convergence of gradient-based algorithms for the Hartree-Fock equations

Antoine Levitt (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The numerical solution of the Hartree-Fock equations is a central problem in quantum chemistry for which numerous algorithms exist. Attempts to justify these algorithms mathematically have been made, notably in [E. Cancès and C. Le Bris, Math. Mod. Numer. Anal. 34 (2000) 749–774], but, to our knowledge, no complete convergence proof has been published, except for the large-Z result of [M. Griesemer and F. Hantsch, Arch. Rational Mech. Anal. (2011) 170]. In this paper, we prove the convergence of...

Convergence of gradient-based algorithms for the Hartree-Fock equations

Antoine Levitt (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The numerical solution of the Hartree-Fock equations is a central problem in quantum chemistry for which numerous algorithms exist. Attempts to justify these algorithms mathematically have been made, notably in [E. Cancès and C. Le Bris, Math. Mod. Numer. Anal. 34 (2000) 749–774], but, to our knowledge, no complete convergence proof has been published, except for the large-Z result of [M. Griesemer and F. Hantsch, Arch. Rational Mech. Anal. (2011) 170]. In this paper, we prove the convergence of...

Convergence of gradient-based algorithms for the Hartree-Fock equations∗

Antoine Levitt (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

The numerical solution of the Hartree-Fock equations is a central problem in quantum chemistry for which numerous algorithms exist. Attempts to justify these algorithms mathematically have been made, notably in [E. Cancès and C. Le Bris, Math. Mod. Numer. Anal. 34 (2000) 749–774], but, to our knowledge, no complete convergence proof has been published, except for the large-Z result of [M. Griesemer and F. Hantsch, Arch. Rational Mech. Anal. (2011) ...

Convergence of mass redistribution method for the one-dimensional wave equation with a unilateral constraint at the boundary

Farshid Dabaghi, Adrien Petrov, Jérôme Pousin, Yves Renard (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

This paper focuses on a one-dimensional wave equation being subjected to a unilateral boundary condition. Under appropriate regularity assumptions on the initial data, a new proof of existence and uniqueness results is proposed. The mass redistribution method, which is based on a redistribution of the body mass such that there is no inertia at the contact node, is introduced and its convergence is proved. Finally, some numerical experiments are reported.

Convergence of some adaptive FEM-BEM coupling for elliptic but possibly nonlinear interface problems

Markus Aurada, Michael Feischl, Dirk Praetorius (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider the symmetric FEM-BEM coupling for the numerical solution of a (nonlinear) interface problem for the 2D Laplacian. We introduce some new a posteriori error estimators based on the (h − h/2)-error estimation strategy. In particular, these include the approximation error for the boundary data, which allows to work with discrete boundary integral operators only. Using the concept of estimator reduction, we prove that the proposed adaptive...

Convergence of some adaptive FEM-BEM coupling for elliptic but possibly nonlinear interface problems

Markus Aurada, Michael Feischl, Dirk Praetorius (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider the symmetric FEM-BEM coupling for the numerical solution of a (nonlinear) interface problem for the 2D Laplacian. We introduce some new a posteriori error estimators based on the (h − h/2)-error estimation strategy. In particular, these include the approximation error for the boundary data, which allows to work with discrete boundary integral operators only. Using the concept of estimator reduction, we prove that the proposed adaptive...

Currently displaying 641 – 660 of 2184