We analyse the convexity property of two classical finite elements and of the associated piecewise polynomial C surfaces. The first one is the piecewise cubic quadrilateral of Fraeijs de Veubeke. The second one is a piecewise quadratic rectangle introduced by Sibson and Thomson and generalized by Sablonnière and Zedek. In both cases, we first study the local problem and then we extend our resul...

We prove the optimal order of convergence for some two-dimensional finite element methods for the Stokes equations. First we consider methods of the Taylor-Hood type: the triangular Pi P2 element and the Qk Qk-\ > k ^ 2 , family of quadrilateral elements. Then we introduce two new low-order methods with piecewise constant approximations for the pressure. The analysis is performed using our macr...

A new simple and accurate four-node quadrilateral element is developed for linear static and dynamic analysis of thin to moderately thick laminated, anisotropic plate/shell structures within the first-order shear deformation theory (FSDT). The element is built by incorporating the strain smoothing method of mesh-free conforming nodal integration into the conventional bilinear four-node quadrila...

A higher order hybrid finite element – method of moments (FEM-MoM) technique for threedimensional analysis and design of radiating and scattering structures is presented. The technique uses generalized parametric hexahedral and quadrilateral elements of arbitrary geometrical orders in conjunction with curland divergence-conforming hierarchical polynomial vector basis functions of arbitrary appr...

This paper describes an MPM formulation using linear quadrilateral elements suitable for soil-structure-interaction problems. The volumetric locking and stress-oscillations are mitigated a reduced integration technique the Gauss scheme, respectively. can be used with both structured unstructured computational meshes. In addition, improved calculation scheme is proposed to obtain accurate contac...

We will prove two conditions for a tangential quadrilateral to be cyclic. According to one of these, a tangential quadrilateral is cyclic if and only if its Newton line is perpendicular to the Newton line of its contact quadrilateral.

Princeton University, Princeton, NJ This paper desribes a technique for finding the numerical solution of the Full Potential equation for steady transonic flow about airfoils. The exterior but finite domain is discretized by breaking it up into triangles. Difference equations are formulated using variational principle and a formula for the derivative in an arbitrary polygon. The iterative schem...

A general adaptive element subdivision technique is presented for the numerical evaluation of weakly singular integrals, which often appear in three-dimensional boundary element analysis equations. In this algorithm, the weakly singular boundary element is broken up into a few sub-elements through a sphere of decreasing radius. The sub-elements involving the singular point are evaluated numeric...