Konvergenzaussagen für Kollokationsverfahren bei elliptischen Randwertaufgaben.
L2 Error Estimates for Finite Elements with Interpolated Boundary Conditions.
L...-Convergence of Collocation and Galerkin Approximations to Linear Two-point Parabolic Systems.
Lösung des Dirichlet Problems bei Jordangebieten mit analytischem Rand durch Interpolation.
Low rank Tucker-type tensor approximation to classical potentials
This paper investigates best rank-(r 1,..., r d) Tucker tensor approximation of higher-order tensors arising from the discretization of linear operators and functions in ℝd. Super-convergence of the best rank-(r 1,..., r d) Tucker-type decomposition with respect to the relative Frobenius norm is proven. Dimensionality reduction by the two-level Tucker-to-canonical approximation is discussed. Tensor-product representation of basic multi-linear algebra operations is considered, including inner, outer...
Mathematical analysis of a spectral hyperviscosity LES model for the simulation of turbulent flows
This paper presents a model based on spectral hyperviscosity for the simulation of 3D turbulent incompressible flows. One particularity of this model is that the hyperviscosity is active only at the short velocity scales, a feature which is reminiscent of Large Eddy Simulation models. We propose a Fourier–Galerkin approximation of the perturbed Navier–Stokes equations and we show that, as the cutoff wavenumber goes to infinity, the solution of the model converges (up to subsequences) to a weak solution...
Mathematical analysis of a spectral hyperviscosity LES model for the simulation of turbulent flows
This paper presents a model based on spectral hyperviscosity for the simulation of 3D turbulent incompressible flows. One particularity of this model is that the hyperviscosity is active only at the short velocity scales, a feature which is reminiscent of Large Eddy Simulation models. We propose a Fourier–Galerkin approximation of the perturbed Navier–Stokes equations and we show that, as the cutoff wavenumber goes to infinity, the solution of the model converges (up to subsequences) to a weak...
Mathematical approach and numerical analysis to the fundamental solutions method of Dirichlet problem.
Mixed finite element approximation of an MHD problem involving conducting and insulating regions : the 2D case
We show that the Maxwell equations in the low frequency limit, in a domain composed of insulating and conducting regions, has a saddle point structure, where the electric field in the insulating region is the Lagrange multiplier that enforces the curl-free constraint on the magnetic field. We propose a mixed finite element technique for solving this problem, and we show that, under mild regularity assumption on the data, Lagrange finite elements can be used as an alternative to edge elements.
Mixed Finite Element approximation of an MHD problem involving conducting and insulating regions: the 2D case
We show that the Maxwell equations in the low frequency limit, in a domain composed of insulating and conducting regions, has a saddle point structure, where the electric field in the insulating region is the Lagrange multiplier that enforces the curl-free constraint on the magnetic field. We propose a mixed finite element technique for solving this problem, and we show that, under mild regularity assumption on the data, Lagrange finite elements can be used as an alternative to edge elements.
Mortar spectral element discretization of the Laplace and Darcy equations with discontinuous coefficients
This paper deals with the mortar spectral element discretization of two equivalent problems, the Laplace equation and the Darcy system, in a domain which corresponds to a nonhomogeneous anisotropic medium. The numerical analysis of the discretization leads to optimal error estimates and the numerical experiments that we present enable us to verify its efficiency.
Mortar spectral method in axisymmetric domains
We consider the Laplace equation posed in a three-dimensional axisymmetric domain. We reduce the original problem by a Fourier expansion in the angular variable to a countable family of two-dimensional problems. We decompose the meridian domain, assumed polygonal, in a finite number of rectangles and we discretize by a spectral method. Then we describe the main features of the mortar method and use the algorithm Strang Fix to improve the accuracy of our discretization.
Mortar spectral method in axisymmetric domains
We consider the Laplace equation posed in a three-dimensional axisymmetric domain. We reduce the original problem by a Fourier expansion in the angular variable to a countable family of two-dimensional problems. We decompose the meridian domain, assumed polygonal, in a finite number of rectangles and we discretize by a spectral method. Then we describe the main features of the mortar method and use the algorithm Strang Fix to improve the accuracy...
Multigrid Methods for Boundary Integral Equations.
Normic inequality of two-dimensional viscosity operator.
Numerical analysis of the planewave discretization of some orbital-free and Kohn-Sham models
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...
Numerical analysis of the planewave discretization of some orbital-free and Kohn-Sham models
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...
Numerical Approximation of a Fractional-In-Space Diffusion Equation, I
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...
On boundary integral equations of the first kind for the bi-laplacian in a polygonal plane domain
On convergence of the polynomial collocation method for singular integral equations and periodic pseudodifferential equations.