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Displaying 481 –
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604
In this paper, we carry out the numerical analysis of a distributed optimal control problem governed by a quasilinear elliptic equation of non-monotone type. The goal is to prove the strong convergence of the discretization of the problem by finite elements. The main issue is to get error estimates for the discretization of the state equation. One of the difficulties in this analysis is that, in spite of the partial differential equation has a unique solution for any given control, the uniqueness...
In this paper, we carry out the numerical analysis of a
distributed optimal control problem governed by a quasilinear
elliptic equation of non-monotone type. The goal is to prove the
strong convergence of the discretization of the problem by finite
elements. The main issue is to get error estimates for the
discretization of the state equation. One of the difficulties in
this analysis is that, in spite of the partial differential
equation has a unique solution for any given control, the
uniqueness...
Many problems in quantum chemistry deal with the computation of fundamental or excited states of molecules and lead to the resolution of eigenvalue problems. One of the major difficulties in these computations lies in the very large dimension of the systems to be solved. Indeed these eigenfunctions depend on variables where stands for the number of particles (electrons and/or nucleari) in the molecule. In order to diminish the size of the systems to be solved, the chemists have proposed many...
Many problems in quantum
chemistry deal with the computation of fundamental or excited states of
molecules and lead to the resolution of eigenvalue problems. One of the
major difficulties in these computations lies in the very large
dimension of the systems to be solved. Indeed these eigenfunctions depend
on 3n variables where n stands for the number of particles
(electrons and/or nucleari) in the molecule. In order to diminish the size
of the systems to be solved, the chemists have proposed...
The present paper deals with solving the general biharmonic problem by the finite element method using curved triangular finit -elements introduced by Ženíšek. The effect of numerical integration is analysed in the case of mixed boundary conditions and sufficient conditions for the uniform -ellipticity are found.
The Method of Fundamental Solutions (MFS) is a boundary-type meshless method for the solution of certain elliptic boundary value problems. In this work, we investigate the properties of the matrices that arise when the MFS is applied to the Dirichlet problem for Laplace’s equation in a disk. In particular, we study the behaviour of the eigenvalues of these matrices and the cases in which they vanish. Based on this, we propose a modified efficient numerical algorithm for the solution of the problem...
The Method of Fundamental Solutions (MFS) is a boundary-type
meshless method for the solution of certain elliptic boundary
value problems. In this work, we investigate the properties of the
matrices that arise when the MFS is applied to the
Dirichlet problem for Laplace's equation in a disk. In particular,
we study the behaviour of the eigenvalues of these matrices and
the cases in which they vanish. Based on this, we propose a
modified efficient numerical algorithm for the solution of the
problem...
In this article, we provide a priorierror estimates for the spectral and pseudospectral Fourier (also called planewave) discretizations of the periodic Thomas-Fermi-von Weizsäcker (TFW) model and for the spectral discretization of the periodic Kohn-Sham model, within the local density approximation (LDA). These models allow to compute approximations of the electronic ground state energy and density of molecular systems in the condensed phase. The TFW model is strictly convex with respect to the...
In this article, we provide a priori error estimates for the spectral and
pseudospectral Fourier (also called planewave) discretizations of the
periodic Thomas-Fermi-von Weizsäcker (TFW) model and for the spectral
discretization of the periodic Kohn-Sham
model, within the local density approximation (LDA). These models
allow to compute approximations of the electronic ground state energy and density
of molecular systems in the condensed phase. The TFW model is strictly
convex with respect to the...
A conceptual numerical strategy for rate-independent processes in the
energetic formulation is proposed and its convergence is proved under various
rather mild data qualifications. The novelty is that we obtain convergence of
subsequences of space-time discretizations even in case where the limit
problem does not have a unique solution and we need no
additional assumptions on higher regularity of the limit solution.
The variety of general perspectives thus
obtained is illustrated on several...
2000 Mathematics Subject Classification: 26A33 (primary), 35S15In this paper, a space fractional diffusion equation (SFDE) with nonhomogeneous
boundary conditions on a bounded domain is considered. A
new matrix transfer technique (MTT) for solving the SFDE is proposed.
The method is based on a matrix representation of the fractional-in-space
operator and the novelty of this approach is that a standard discretisation
of the operator leads to a system of linear ODEs with the matrix raised
to the...
2000 Mathematics Subject Classification: 26A33 (primary), 35S15 (secondary)This paper provides a new method and corresponding numerical schemes
to approximate a fractional-in-space diffusion equation on a bounded domain
under boundary conditions of the Dirichlet, Neumann or Robin type.
The method is based on a matrix representation of the fractional-in-space
operator and the novelty of this approach is that a standard discretisation
of the operator leads to a system of linear ODEs with the matrix...
We introduce and analyze a numerical strategy to approximate effective coefficients in stochastic homogenization of discrete elliptic equations. In particular, we consider the simplest case possible: An elliptic equation on the d-dimensional lattice with independent and identically distributed conductivities on the associated edges. Recent results by Otto and the author quantify the error made by approximating the homogenized coefficient by the averaged energy of a regularized corrector (with...
We introduce and analyze a numerical strategy
to approximate effective coefficients in stochastic homogenization of discrete elliptic
equations. In particular, we consider the simplest case possible: An elliptic equation on
the d-dimensional lattice
with independent and identically distributed conductivities on the associated edges.
Recent results by Otto and the author quantify the error made by approximating
the homogenized coefficient by the averaged energy of a regularized
corrector (with...
A new set of nonlocal boundary conditions is proposed for the higher modes of the 3D inviscid primitive equations. Numerical schemes using the splitting-up method are proposed for these modes. Numerical simulations of the full nonlinear primitive equations are performed on a nested set of domains, and the results are discussed.
A new set of nonlocal boundary conditions is proposed for the higher modes of the 3D inviscid primitive equations. Numerical schemes using the splitting-up method are proposed for these modes. Numerical simulations of the full nonlinear primitive equations are performed on a nested set of domains, and the results are discussed.
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