Interpolation operators map a function u to an element Iu of a finite element space. Unlike more general approximation operators, interpolants are defined locally. Estimates of the interpolation error, i.e., the difference u− Iu, are of utmost importance in numerical analysis. These estimates depend on the size of the finite elements, the polynomial degree employed, and the regularity of u. In ...

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...

Whereas the higher-order versions of the finite element method (p and hp-versions) are fairly well established as highly efficient methods for monitoring and controlling the discretization error in linear problems, little has been done to exploit their benefits in elasto-plastic structural analysis. In this paper, we discuss which aspects of incremental elasto-plastic finite element analysis ar...

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...

This paper is the first in a series devoted to the approximation theory of the p-version of the finite element method in three dimensions. In this paper, we introduce the Jacobi-weighted Besov and Sobolev spaces in the three-dimensional setting and analyze the approximability of functions in the framework of these spaces. In particular, the Jacobi-weighted Besov and Sobolev spaces with three di...