Abschnittzerlegungen bei oberen Schranken für Eigenwerte von Operatorpolynomen.
Acceleration of two-grid stabilized mixed finite element method for the Stokes eigenvalue problem
This paper provides an accelerated two-grid stabilized mixed finite element scheme for the Stokes eigenvalue problem based on the pressure projection. With the scheme, the solution of the Stokes eigenvalue problem on a fine grid is reduced to the solution of the Stokes eigenvalue problem on a much coarser grid and the solution of a linear algebraic system on the fine grid. By solving a slightly different linear problem on the fine grid, the new algorithm significantly improves the theoretical error...
An a posteriori Error Estimation of the Rayleigh-Ritz Eigenvalues.
An Iteration Method for Studying the Bifurcation of Solutions of the Nonlinear Equations, L(...) u + ..R (..., u) = 0 .
An operator method for a numerical quadrature finite element approximation for a class of second-order elliptic eigenvalue problems in composite structures
Analysis of a coupled BEM/FEM eigensolver for the hydroelastic vibrations problem
A coupled finite/boundary element method to approximate the free vibration modes of an elastic structure containing an incompressible fluid is analyzed in this paper. The effect of the fluid is taken into account by means of one of the most usual procedures in engineering practice: an added mass formulation, which is posed in terms of boundary integral equations. Piecewise linear continuous elements are used to discretize the solid displacements and the fluid-solid interface variables. Spectral...
Analysis of a coupled BEM/FEM eigensolver for the hydroelastic vibrations problem
A coupled finite/boundary element method to approximate the free vibration modes of an elastic structure containing an incompressible fluid is analyzed in this paper. The effect of the fluid is taken into account by means of one of the most usual procedures in engineering practice: an added mass formulation, which is posed in terms of boundary integral equations. Piecewise linear continuous elements are used to discretize the solid displacements and the fluid-solid interface variables....
Analysis of an algorithm for computing electromagnetic Bloch modes using Nedelec spaces.
Approximation and eigenvalue extrapolation of Stokes eigenvalue problem by nonconforming finite element methods
In this paper we analyze the stream function-vorticity-pressure method for the Stokes eigenvalue problem. Further, we obtain full order convergence rate of the eigenvalue approximations for the Stokes eigenvalue problem based on asymptotic error expansions for two nonconforming finite elements, and . Using the technique of eigenvalue error expansion, the technique of integral identities and the extrapolation method, we can improve the accuracy of the eigenvalue approximations.
Approximation du spectre d'un operateur linearie; application aux operateurs differentiels elliptiqes non autoadjoints.
Approximation in Variationally Posed Eigenvalue Problems.
Approximation of a Nondifferentiable Nonlinear Problem Related to MHD Equilibria.
Approximation of an eigenvalue problem associated with the Stokes problem by the stream function-vorticity-pressure method
By means of eigenvalue error expansion and integral expansion techniques, we propose and analyze the stream function-vorticity-pressure method for the eigenvalue problem associated with the Stokes equations on the unit square. We obtain an optimal order of convergence for eigenvalues and eigenfuctions. Furthermore, for the bilinear finite element space, we derive asymptotic expansions of the eigenvalue error, an efficient extrapolation and an a posteriori error estimate for the eigenvalue. Finally,...
Approximation of solution branches for semilinear bifurcation problems
Approximation of solution branches for semilinear bifurcation problems
This note deals with the approximation, by a P1 finite element method with numerical integration, of solution curves of a semilinear problem. Because of both mixed boundary conditions and geometrical properties of the domain, some of the solutions do not belong to H2. So, classical results for convergence lead to poor estimates. We show how to improve such estimates with the use of weighted Sobolev spaces together with a mesh “a priori adapted” to the singularity. For the H1 or L2-norms, we...
Approximation of solution branches of nonlinear equations
Approximation of the Sobolev trace constant.
Approximation von Eigenwertproblemen bei nichtlinearer Parameterabhängigkeit.
Asymptotic behaviour and numerical approximation of optimal eigenvalues of the Robin laplacian
We consider the problem of minimising the nth-eigenvalue of the Robin Laplacian in RN. Although for n = 1,2 and a positive boundary parameter α it is known that the minimisers do not depend on α, we demonstrate numerically that this will not always be the case and illustrate how the optimiser will depend on α. We derive a Wolf–Keller type result for this problem and show that optimal eigenvalues grow at most with n1/N, which is in sharp contrast with the Weyl asymptotics for a fixed domain. We further...
Asymptotic lower bounds for eigenvalues by nonconforming finite element methods.