Efficient solution of symmetric eigenvalue problems using multigrid preconditioners in the locally optimal block conjugate gradient method.
Eigenvalue approximations by mixed methods
Eigenvalues and eigenfunctions of the Laplace operator on an equilateral triangle for the discrete case
A discretized boundary value problem for the Laplace equation with the Dirichlet and Neumann boundary conditions on an equilateral triangle with a triangular mesh is transformed into a problem of the same type on a rectangle. Explicit formulae for all eigenvalues and all eigenfunctions are given.
Eine Aussage zur L...-Stabilität und zur genauen Konvergenzordnung der H...-Projektionen.
Einige Eigenschaften der Lösung der Wellengleichung mit der Korrektion von Rayleigh
Electrowetting of a 3D drop: numerical modelling with electrostatic vector fields
The electrowetting process is commonly used to handle very small amounts of liquid on a solid surface. This process can be modelled mathematically with the help of the shape optimization theory. However, solving numerically the resulting shape optimization problem is a very complex issue, even for reduced models that occur in simplified geometries. Recently, the second author obtained convincing results in the 2D axisymmetric case. In this paper, we propose and analyze a method that is suitable...
Element-oriented and edge-oriented local error estimators for nonconforming finite element methods
Éléments finis et l'estimation de l'erreur intérieur de la convergence
Éléments finis et problèmes elliptiques dégénérés
Éléments finis mixtes incompressibles pour l'équation de Stokes dans IR3 .
Elliptic grids with nearly uniform cell area and line spacing.
Embedding and a priori wavelet-adaptivity for Dirichlet problems
Embedding and a priori wavelet-adaptivity for Dirichlet problems
The accuracy of the domain embedding method from [A. Rieder, Modél. Math. Anal. Numér.32 (1998) 405-431] for the solution of Dirichlet problems suffers under a coarse boundary approximation. To overcome this drawback the method is furnished with an a priori (static) strategy for an adaptive approximation space refinement near the boundary. This is done by selecting suitable wavelet subspaces. Error estimates and numerical experiments validate the proposed adaptive scheme. In contrast to similar,...
En ε-uniformly convergent non-conforming finite element method for a singularly perturbed elliptic problem in two dimensions
Energetics and switching of quasi-uniform states in small ferromagnetic particles
We present a numerical algorithm to solve the micromagnetic equations based on tangential-plane minimization for the magnetization update and a homothethic-layer decomposition of outer space for the computation of the demagnetization field. As a first application, detailed results on the flower-vortex transition in the cube of Micromagnetic Standard Problem number 3 are obtained, which confirm, with a different method, those already present in the literature, and validate our method and code. We...
Energetics and switching of quasi-uniform states in small ferromagnetic particles
We present a numerical algorithm to solve the micromagnetic equations based on tangential-plane minimization for the magnetization update and a homothethic-layer decomposition of outer space for the computation of the demagnetization field. As a first application, detailed results on the flower-vortex transition in the cube of Micromagnetic Standard Problem number 3 are obtained, which confirm, with a different method, those already present in the literature, and validate our method and...
Energy error estimates for a linear scheme to approximate nonlinear parabolic problems
Energy norm error estimates and convergence analysis for a stabilized Maxwell's equations in conductive media
The aim of this article is to investigate the well-posedness, stability of solutions to the time-dependent Maxwell's equations for electric field in conductive media in continuous and discrete settings, and study convergence analysis of the employed numerical scheme. The situation we consider would represent a physical problem where a subdomain is emerged in a homogeneous medium, characterized by constant dielectric permittivity and conductivity functions. It is well known that in these homogeneous...
Enrichissement des interpolations d’éléments finis en utilisant des méthodes sans maillage
Les méthodes sans maillage emploient une interpolation associée à un ensemble de particules : aucune information concernant la connectivité ne doit être fournie. Un des atouts de ces méthodes est que la discrétisation peut être enrichie d’une façon très simple, soit en augmentant le nombre de particules (analogue à la stratégie de raffinement ), soit en augmentant l’ordre de consistance (analogue à la stratégie de raffinement ). Néanmoins, le coût du calcul des fonctions d’interpolation est très...
Enrichissement des interpolations d'éléments finis en utilisant des méthodes sans maillage
Les méthodes sans maillage emploient une interpolation associée à un ensemble de particules : aucune information concernant la connectivité ne doit être fournie. Un des atouts de ces méthodes est que la discrétisation peut être enrichie d'une façon très simple, soit en augmentant le nombre de particules (analogue à la stratégie de raffinement h), soit en augmentant l'ordre de consistance (analogue à la stratégie de raffinement p). Néanmoins, le coût du calcul des fonctions d'interpolation est...