Displaying similar documents to “Computation of 3D vertex singularities for linear elasticity : error estimates for a finite element method on graded meshes”

Computation of 3D vertex singularities for linear elasticity: Error estimates for a finite element method on graded meshes

Thomas Apel, Anna-Margarete Sändig, Sergey I. Solov'ev (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

This paper is concerned with the computation of 3D vertex singularities of anisotropic elastic fields with Dirichlet boundary conditions, focusing on the derivation of error estimates for a finite element method on graded meshes. The singularities are described by eigenpairs of a corresponding operator pencil on spherical polygonal domains. The main idea is to introduce a modified quadratic variational boundary eigenvalue problem which consists of two self-adjoint, positive...

Nonconforming finite element approximations of the Steklov eigenvalue problem and its lower bound approximations

Qin Li, Qun Lin, Hehu Xie (2013)

Applications of Mathematics

Similarity:

The paper deals with error estimates and lower bound approximations of the Steklov eigenvalue problems on convex or concave domains by nonconforming finite element methods. We consider four types of nonconforming finite elements: Crouzeix-Raviart, Q 1 rot , E Q 1 rot and enriched Crouzeix-Raviart. We first derive error estimates for the nonconforming finite element approximations of the Steklov eigenvalue problem and then give the analysis of lower bound approximations. Some numerical results are presented...

The effect of reduced integration in the Steklov eigenvalue problem

Maria G. Armentano (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Similarity:

In this paper we analyze the effect of introducing a numerical integration in the piecewise linear finite element approximation of the Steklov eigenvalue problem. We obtain optimal order error estimates for the eigenfunctions when this numerical integration is used and we prove that, for singular eigenfunctions, the eigenvalues obtained using this reduced integration are better approximations than those obtained using exact integration when the mesh size is small enough.