Electrical impedance tomography (EIT) is a non-invasive imaging technique where a conductivity distribution in a domain is reconstructed from boundary voltage measurements. The voltage data are generated by injecting currents into the domain. This is an ill-conditioned non-linear inverse problem. Small measurement or forward modeling errors can lead to unbounded fluctuations in the reconstructi...

In this paper, we use the hybrid h-p version of the finite element method to study the effect of an open transverse crack on the vibratory behavior of rotors, the one-dimensional finite element Euler-Bernoulli beam is used for modeling the rotor, the shape functions used are the Hermite cubic functions coupled to the special Legendre polynomials of Rodrigues. The global matrices of the equation...

Already very early Prof. Oleg Zienkiewicz pointed to potential advantages of using higher order instead of low order shape functions for the finite element method [1]. The p-version as a systematic extension process of the finite element method leaves the mesh unchanged and increases the polynomial degree of the shape functions locally or globally [5]. It has turned out to be a very efficient d...

We consider higher order mixed finite element methods for the incompressible Stokes or Navier-Stokes equations with Qr-elements for the velocity and discontinuous Pr−1-elements for the pressure where the order r can vary from element to element between 2 and a fixed bound r∗. We prove the inf-sup condition uniformly with respect to the meshwidth h on general quadrilateral and hexahedral meshes ...

Polynomial extensions play a vital role in the analysis of the p and h-p FEM and the spectral element method. We construct explicitly polynomial extensions on standard elements: cubes, triangular prisms and pyramids, which together with the extension on tetrahedrons are used by the p and h-p FEM in three dimensions. These extensions are proved to be stable and compatible with FEM subspaces on t...

A new nite element method for elliptic problems with locally periodic microstructure of length " > 0 is developed and analyzed. It is shown that the method converges, as " ! 0, to the solution of the homogenized problem with optimal order in " and exponentially in the number of degrees of freedom independent of " > 0. The computational work of the method is bounded independently of ". Numerical...