Based on classical plate theory, standard and spectral finite element methods are extended for vibration and dynamic stability of axially moving thin plates subjected to in-plane forces. The formulation of the standard method earned through Hamilton’s principle is independent of element type. But for solving numerical examples, an isoparametric quadrilateral element is developed using Lagrange ...

Based on classical plate theory, standard and spectral finite element methods are extended for vibration and dynamic stability of axially moving thin plates subjected to in-plane forces. The formulation of the standard method earned through Hamilton’s principle is independent of element type. But for solving numerical examples, an isoparametric quadrilateral element is developed using Lagrange ...

The aim of this paper is to investigate finite element methods for the solution of elliptic partial differential equations on implicitely defined surfaces. The problem of solving such equations without triangulating surfaces is of increasing importance in various applications, and their discretization has recently been investigated in the framework of finite difference methods. For the two most...

In the paper a recent enhancement to the open source package SfePy (Simple Finite Elements in Python, http://sfepy.org) is introduced, namely the addition of another numerical discretization scheme, the isogeometric analysis, to the original implementation based on the nowadays standard and wellestablished numerical solution technique, the finite element method. The isogeometric removes the nee...

Abstract. We consider the finite element approximation of the Laplacian operator with the homogeneous Dirichlet boundary condition, and study the corresponding Lagrange interpolation in the context of finite element superconvergence. For ddimensional Qk-type elements with d ≥ 1 and k ≥ 1, we prove that the interpolation points must be the Lobatto points if the Lagrange interpolation and the fin...

Electrical impedance tomography is an imaging method, with which volumetric images of conductivity are produced by injecting electrical current and measuring boundary voltages. It has the potential to become a portable non-invasive medical imaging technique. Until now, implementations have neglected anisotropy even though human tissues such as bone, muscle and brain white matter are markedly an...

Superconvergence results and several gradient recovery methods of finite element methods in flat spaces are generalized to the surface linear finite element method for the LaplaceBeltrami equation on general surfaces with mildly structured triangular meshes. For a large class of practically useful grids, the surface linear finite element solution is proven to be superclose to an interpolant of ...