The aim of this paper is to develop a new class of finite elements on quadrilaterals and hexahedra. The degrees of freedom are the values at the vertices and the approximation is polynomial on each element K. In general, with this kind of finite elements, the resolution of second order elliptic problems leads to non-conforming approximations.Degrees of freedom are the same than those of isopara...

Article history: Received 21 April 2009 Received in revised form 23 June 2009 Accepted 23 July 2009 Available online 29 July 2009

Lagrange-type hexahedral finite elements enable efficient approximation of various types of curved and flat geometrical shapes within the large-domain modeling framework. We have investigated the accuracy and limitations of the geometrical approximations of specific geometrical shapes and analyzed its impact on the accuracy of the finite element solution. Our conclusions are verified computatio...

A multiphase-field model for the description of coalescence in a binary alloy is solved numerically using adaptive finite elements with high aspect ratio. The unknown of the multiphase-field model are the three phase fields (solid phase 1, solid phase 2, and liquid phase), a Lagrange multiplier and the concentration field. An Euler implicit scheme is used for time discretization, together with ...

The computation of optical modes inside axisymmetric cavity resonators with a general spatial permittivity profile is a formidable computational task. In order to avoid spurious modes the vector Helmholtz equations are discretised by a mixed finite element approach. We formulate the method for first and second order Nédélec edge and Lagrange nodal elements. We discuss how to accurately compute ...

We prove that constant functions are the unique real-valued maximizers for all L2−L2n adjoint Fourier restriction inequalities on unit sphere Sd−1⊂Rd, d∈{3,4,5,6,7}, where n⩾3 is an integer. The proof uses tools from probability theory, Lie functional analysis, and theory of special functions. It also relies general solutions underlying Euler–Lagrange equation being smooth, a fact independent i...

The stability properties of simple element choices for the mixed formulation of the Laplacian are investigated numerically. The element choices studied use vector Lagrange elements, i.e., the space of continuous piecewise polynomial vector fields of degree at most r , for the vector variable, and the divergence of this space, which consists of discontinuous piecewise polynomials of one degree l...

Domain decomposition techniques provide a powerful tool for the numerical approximation of partial differential equations. We consider mortar techniques with dual Lagrange multiplier spaces to couple different discretization schemes. It is well known that the discretization error for linear mortar finite elements in the energy norm is of order h. Here, we apply these techniques to curvilinear b...

This paper extends the inverse substructuring (IS) approach to state-space domain and presents a novel (SSS) technique that embeds dynamics of connecting elements (CEs) in Lagrange Multiplier State-Space Substructuring (LM-SSS) formulation via compatibility relaxation. coupling makes it possible incorporate into LM-SSS are suitable for being characterized by (e.g. rubber mounts) simply using in...

in this research project, the nitrito nitro isomerization of [co (nh3)5no2]f2 complex has been studied. isomerization of this complex in the solid state follows a first order kinetics. the rate of isomerization at different temperatures was determined using a fourier transform lnfrared spectrophotometer. ? and ? are calculated at 298 k. the infrared, visible and ultraviolet spectra of this comp...