Hierarchical bases of arbitrary order for H(div)-conforming triangular and tetrahedral elements are constructed with the goal of improving the conditioning of the mass and stiffness matrices. For the basis with the triangular element, it is found numerically that the conditioning is acceptable up to the approximation of order four, and is better than a corresponding basis in the dissertation by...

This contribution deals with the numerical solution of elliptic boundary value problems with unilateral boundary conditions using a fictitious domain method. Any fictitious domain formulation [2] extends the original problem defined in a domain ω to a new (fictitious) domain Ω with a simple geometry (e.g. a box) which contains ω. The main advantage consists in possibility to use a uniform mesh ...

A posteriori error estimators based on auxiliary subspace techniques for second order elliptic problems in Rd (d ≥ 2) are considered. In this approach, the solution of a global problem is utilized as the error estimator. As the continuity and coercivity of the problem trivially leads to an efficiency bound, the main focus of this paper is to derive an analogous effectivity bound and to determin...

We discuss a new approach for the construction of the secondlevel Neumann-Neumann coarse space. Our method is based on an inexpensive and parallel analysis of the lower part spectrum of each subdomain stiffness matrix. We show that the method is flexible enough to converge fast on nonstandard decompositions and various types of finite elements used in structural analysis packages.

The electromechanical interaction in electric machines induces additional forces between the rotor and stator. To study this interaction, a simple electromechanical model was developed. The mechanical behaviour was modelled by the Jeffcott rotor. The electromagnetic forces were described by a simple parametric model including two electormagnetic variables. The aim of the study was to investigat...

This paper proposes a new method, in the frequency domain, to define absorbing boundary conditions for general two-dimensional problems. The main feature of the method is that it can obtain boundary conditions from the discretized equations without much knowledge of the analytical behavior of the solutions and is thus very general. It is based on the computation of waves in periodic structures ...

The non-local diffusion model provides an appropriate description of the deformation of a continuous body involving discontinuities or other singularities, which cannot be described properly by classical theory of solid mechanics. However, because the non-local nature of the non-local diffusion operator, the numerical methods for non-local diffusion model generate dense or even full stiffness m...

In this contribution we analyze a generalization of the heterogeneous multiscale finite element method for elliptic homogenization problems in perforated domains. The method was originally introduced by E and Engquist (Commun Math Sci 1(1):87–132, 2003) for homogenization problems in fixed domains. It is based on a standard finite element approach on the macroscale, where the stiffness matrix i...

A two-level preconditioning method for the solution of (locally) refined finite element schemes using triangle meshes is introduced. In the isotropic SPD case, it is shown that the condition number of the preconditioned stiffness matrix is bounded uniformly for all sufficiently regular triangulations. This is also verified numerically for an isotropic diffusion problem with highly discontinuous...

This paper discusses the stability of 2D frictionless grasps and combining stability of frictional and frictionless grasps from the viewpoint of potential energy method. In many works related to the frictionless grasp, each finger is replaced by one directional virtual spring along the normal at the contact point. However, this condition is not accurate, because the frictionless condition does ...