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Displaying 1041 –
1060 of
2193
This paper deals with the numerical study of a nonlinear, strongly anisotropic heat equation. The use of standard schemes in this situation leads to poor results, due to the high anisotropy. An Asymptotic-Preserving method is introduced in this paper, which is second-order accurate in both, temporal and spacial variables. The discretization in time is done using an L-stable Runge−Kutta scheme. The convergence of the method is shown to be independent of the anisotropy parameter , and this for fixed...
We propose and examine a simple averaging formula for the gradient of linear finite elements in whose interpolation order in the -norm is for and nonuniform triangulations. For elliptic problems in we derive an interior superconvergence for the averaged gradient over quasiuniform triangulations. A numerical example is presented.
In this work, we analyze hierarchic hp-finite element discretizations of the full, three-dimensional
plate problem. Based on two-scale asymptotic expansion of the three-dimensional solution, we give
specific mesh design principles for the hp-FEM which allow to resolve the three-dimensional boundary
layer profiles at robust, exponential rate.
We prove that, as the plate half-thickness ε tends to zero, the hp-discretization is consistent
with the three-dimensional solution to any power of ε in...
We propose and analyze a domain decomposition method on non-matching grids
for partial differential equations with non-negative
characteristic form. No weak or strong continuity of the finite
element functions, their normal derivatives, or linear
combinations of the two is imposed across the boundaries of the subdomains.
Instead, we employ suitable bilinear forms defined on the common
interfaces, typical of discontinuous Galerkin
approximations.
We prove an error bound which is optimal with respect...
In this paper a strategy is investigated for the spatial coupling of an asymptotic
preserving scheme with the asymptotic limit model, associated to a singularly perturbed,
highly anisotropic, elliptic problem. This coupling strategy appears to be very
advantageous as compared with the numerical discretization of the initial singular
perturbation model or the purely asymptotic preserving scheme introduced in previous works [3, 5]. The model problem addressed...
We present a hybrid OpenMP/MPI parallelization of the finite element method that is suitable to make use of modern high performance computers. These are usually built from a large bulk of multi-core systems connected by a fast network. Our parallelization method is based firstly on domain decomposition to divide the large problem into small chunks. Each of them is then solved on a multi-core system using parallel assembling, solution and error estimation. To make domain decomposition for both, the...
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....
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. 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...
This paper is devoted to the study of a turbulent circulation model. Equations are derived from the “Navier-Stokes turbulent kinetic energy” system. Some simplifications are performed but attention is focused on non linearities linked to turbulent eddy viscosity . The mixing length acts as a parameter which controls the turbulent part in . The main theoretical results that we have obtained concern the uniqueness of the solution for bounded eddy viscosities and small values of and its asymptotic...
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