Une méthode nodale appliquée à un problème de diffusion à coefficients généralisés
Une méthode nodale appliquée à un problème de diffusion à coefficients généralisés
In this paper, we consider second order neutrons diffusion problem with coefficients in L∞(Ω). Nodal method of the lowest order is applied to approximate the problem's solution. The approximation uses special basis functions [1] in which the coefficients appear. The rate of convergence obtained is O(h2) in L2(Ω), with a free rectangular triangulation.
Uniform convergence of local multigrid methods for the time-harmonic Maxwell equation
For the efficient numerical solution of indefinite linear systems arising from curl conforming edge element approximations of the time-harmonic Maxwell equation, we consider local multigrid methods (LMM) on adaptively refined meshes. The edge element discretization is done by the lowest order edge elements of Nédélec’s first family. The LMM features local hybrid Hiptmair smoothers of Jacobi and Gauss–Seidel type which are performed only on basis functions associated with newly created edges/nodal...
Uniform convergence of local multigrid methods for the time-harmonic Maxwell equation∗
For the efficient numerical solution of indefinite linear systems arising from curl conforming edge element approximations of the time-harmonic Maxwell equation, we consider local multigrid methods (LMM) on adaptively refined meshes. The edge element discretization is done by the lowest order edge elements of Nédélec’s first family. The LMM features local hybrid Hiptmair smoothers of Jacobi and Gauss–Seidel type which are performed only on basis functions associated with newly created edges/nodal...
Uniform convergence of monotone iterative methods for semilinear singularly perturbed problems of elliptic and parabolic types.
Uniformly convergent adaptive methods for a class of parametric operator equations∗
We derive and analyze adaptive solvers for boundary value problems in which the differential operator depends affinely on a sequence of parameters. These methods converge uniformly in the parameters and provide an upper bound for the maximal error. Numerical computations indicate that they are more efficient than similar methods that control the error in a mean square sense.
Uniformly convergent adaptive methods for a class of parametric operator equations∗
We derive and analyze adaptive solvers for boundary value problems in which the differential operator depends affinely on a sequence of parameters. These methods converge uniformly in the parameters and provide an upper bound for the maximal error. Numerical computations indicate that they are more efficient than similar methods that control the error in a mean square sense.
Uniformly Convergent Difference Schemes for Singularly Perturbed Parabolic Diffusion-Convection Problems Without Turning Points.
Uniformly stable mixed hp-finite elements on multilevel adaptive grids with hanging nodes
We consider a family of quadrilateral or hexahedral mixed hp-finite elements for an incompressible flow problem with Qr-elements for the velocity and discontinuous -elements for the pressure where the order r can vary from element to element between 2 and an arbitrary bound. For multilevel adaptive grids with hanging nodes and a sufficiently small mesh size, we prove the inf-sup condition uniformly with respect to the mesh size and the polynomial degree.
Unique solvability and stability analysis of a generalized particle method for a Poisson equation in discrete Sobolev norms
Unique solvability and stability analysis is conducted for a generalized particle method for a Poisson equation with a source term given in divergence form. The generalized particle method is a numerical method for partial differential equations categorized into meshfree particle methods and generally indicates conventional particle methods such as smoothed particle hydrodynamics and moving particle semi-implicit methods. Unique solvability is derived for the generalized particle method for the...
Variational approximation of flux in conforming finite element methods for elliptic partial differential equations : a model problem
We consider the approximation of elliptic boundary value problems by conforming finite element methods. A model problem, the Poisson equation with Dirichlet boundary conditions, is used to examine the convergence behavior of flux defined on an internal boundary which splits the domain in two. A variational definition of flux, designed to satisfy local conservation laws, is shown to lead to improved rates of convergence.
Vorzeichenstabile Differenzenverfahren für parabolische Anfangsrandwertaufgaben.
Wavelet approximation methods for pseudodifferential equations: I. Stability and convergence.
Wavelet compression of anisotropic integrodifferential operators on sparse tensor product spaces
For a class of anisotropic integrodifferential operators arising as semigroup generators of Markov processes, we present a sparse tensor product wavelet compression scheme for the Galerkin finite element discretization of the corresponding integrodifferential equations u = f on [0,1]n with possibly large n. Under certain conditions on , the scheme is of essentially optimal and dimension independent complexity (h-1| log h |2(n-1)) without corrupting the convergence or smoothness requirements...
Zur Konvergenz des Peaceman-Rachford-Verfahrens. -On the Convergence of the Peaceman-Rachford Iterative Method.
Zur Konvergenz des Rayleigh-Ritz-Verfahrens bei Eigenwertaufgaben.
Исследование разностной схемы для нелинейний стационарной задачи теории фильтрации
Исследование разностных схем для квазилинейных вырождающихся параболических уравнений
Исследование сходимости разностных схем для квазилинейных эллиптических уравнений с вырождением
Некоторые применения пятиточечной схемы метода прямых