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In the framework of an explicitly correlated formulation of the electronic Schrödinger equation known as the transcorrelated method, this work addresses some fundamental issues concerning the feasibility of eigenfunction approximation by hyperbolic wavelet bases. Focusing on the two-electron case, the integrability of mixed weak derivatives of eigenfunctions of the modified problem and the improvement compared to the standard formulation are discussed. Elements of a discretization of the eigenvalue...
In the framework of an explicitly correlated formulation of the electronic Schrödinger
equation known as the transcorrelated method, this work addresses some fundamental issues
concerning the feasibility of eigenfunction approximation by hyperbolic wavelet bases.
Focusing on the two-electron case, the integrability of mixed weak derivatives of
eigenfunctions of the modified problem and the improvement compared to the standard
formulation are discussed....
We consider the finite element approximation of the identification problem, where one wishes to identify a curve along which a given solution of the boundary value problem possesses some specific property. We prove the convergence of FE-approximation and give some results of numerical tests.
The Mumford-Shah functional for image segmentation is an original approach
of the image segmentation problem, based on a minimal energy criterion. Its
minimization can be seen as a free discontinuity problem and is based on
Γ-convergence and bounded variation functions theories. Some new
regularization results, make possible to imagine a finite element resolution
method. In a first time, the Mumford-Shah functional is
introduced and some existing results are quoted. Then, a
discrete formulation...
To solve the contact problems by using a semismooth Newton method, we shall linearize stiffness and mass matrices as well as contact conditions. The latter are prescribed by means of mortar formulation. In this paper we describe implementation details.
In this work we first focus on the Stochastic Galerkin approximation of the solution u of an elliptic stochastic PDE. We rely on sharp estimates for the decay of the coefficients of the spectral expansion of u on orthogonal polynomials to build a sequence of polynomial subspaces that features better convergence properties compared to standard polynomial subspaces such as Total Degree or Tensor Product. We consider then the Stochastic Collocation method, and use the previous estimates to introduce...
We develop implicit a posteriori error estimators for elliptic boundary value problems. Local problems are formulated for the error and the corresponding Neumann type boundary conditions are approximated using a new family of gradient averaging procedures. Convergence properties of the implicit error estimator are discussed independently of residual type error estimators, and this gives a freedom in the choice of boundary conditions. General assumptions are elaborated for the gradient averaging...
We present an improvement to the direct flux reconstruction technique for equilibrated flux a posteriori error estimates for one-dimensional problems. The verification of the suggested reconstruction is provided by numerical experiments.
In a posteriori error analysis of reduced basis approximations to affinely parametrized partial differential equations, the construction of lower bounds for the coercivity and inf-sup
stability constants is essential. In [Huynh et al., C. R. Acad.
Sci. Paris Ser. I Math.345 (2007) 473–478], the authors presented an efficient
method, compatible with an off-line/on-line strategy, where the on-line computation is reduced to
minimizing a linear functional under a few linear constraints. These constraints...
We present families of scalar nonconforming finite elements of arbitrary
order with optimal approximation properties on quadrilaterals and
hexahedra. Their vector-valued versions together with a discontinuous
pressure approximation of order form inf-sup stable finite element pairs
of order r for the Stokes problem. The well-known elements by Rannacher
and Turek are recovered in the case r=1. A numerical comparison between
conforming and nonconforming discretisations will be given. Since higher
order...
A class of compatible spatial discretizations for solving partial differential equations is presented. A discrete exact sequence framework is developed to classify these methods which include the mimetic and the covolume methods as well as certain low-order finite element methods. This construction ensures discrete analogs of the differential operators that satisfy the identities and theorems of vector calculus, in particular a Helmholtz decomposition theorem for the discrete function spaces. This...
A conformal finite element method is investigated for a dual variational formulation of the biharmonic problem with mixed boundary conditions on domains with piecewise smooth curved boundary. Thus in the problem of elastic plate the bending moments are calculated directly. For the construction of finite elements a vector potential is used together with -elements. The convergence of the method is proved and an algorithm described.
Using the stream function, some finite element subspaces of divergence-free vector functions, the normal components of which vanish on a part of the piecewise smooth boundary, are constructed. Applying these subspaces, an internal approximation of the dual problem for second order elliptic equations is defined.
A convergence of this method is proved without any assumption of a regularity of the solution. For sufficiently smooth solutions an optimal rate of convergence is proved. The internal approximation...
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760 of
1415