The coordinate transformation for quadrilateral isoparametric elements is well-defined in the finite element literature. However, a corresponding inverse transformation is not found. In fact, it has been commonly believed that no explicit solutions to the inverse transformation problem exist. This paper shows that if geometric considerations are used, a complete set of general solutions to the ...

Abstract. A hybrid stress finite volume method is proposed for linear elasticity equations. In this new method, a finite volume formulation is used for the equilibrium equation, and a hybrid stress quadrilateral finite element discretization, with continuous piecewise isoparametric bilinear displacement interpolation and two types of stress approximation modes, is used for the constitutive equa...

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 study focuses on the optimization of the plane structure. Sequential quadratic programming (SQP) will be utilized, which is one of the most efficient methods for solving nonlinearly constrained optimization problems. A new formulation for the second order sensitivity analysis of the two-dimensional finite element will be developed. All the second order required derivatives will be calculat...

Abstract. Superconvergence of the velocity is established for mimetic finite difference approximations of second-order elliptic problems over h2-uniform quadrilateral meshes. The superconvergence result holds for a full tensor coefficient. The analysis exploits the relation between mimetic finite differences and mixed finite element methods via a special quadrature rule for computing the scalar...

Consider a triangulation of the xy plane, and a general surface z = f(x; y). The points of the triangle, when lifted to the surface, form a linear spline approximation to the surface. We are interested in the error between the surface and the linear approximant. In fact, we are interested in building triangulations in the plane such that the induced linear approximant is near-optimal with respe...

In this paper we investigate the structure of flip graphs on non-crossing perfect matchings in plane. Specifically, consider all straight-line a set 2n points that are placed equidistantly unit circle. A operation such matching replaces two edges span an empty quadrilateral with other quadrilateral, and is called centered if contains center The graph Gn has those as vertices, edge between any d...