A boundary element method has been developed for the analysis of 3D eddy current problems. This method is based on the boundary integral equation formulation with equivalent electric and magnetic currents and electric charge as unknowns. Linear shape functions, defined parametrically over a quadrilateral element, have been selected for the Galerkin’s method.

In this paper, a locally stabilized finite element formulation of the Stokes problem is analyzed. A macroelement condition which is sufficient for the stability of (locally stabilized) mixed methods based on a piecewise constant pressure approximation is introduced. By satisfying this condition, the stability of the Q\Pq, quadrilateral, and the P\-Pq triangular element, can be established.

A symmetric finite volume element scheme on quadrilateral grids is established for a class of elliptic problems. The asymptotic error expansion of finite volume element approximation is obtained under rectangle grids, which in turn yields the error estimates and superconvergence of the averaged derivatives. Numerical examples confirm our theoretical analysis.

In this paper, we examine the influence of numerical integration on finite element methods using quadrilateral or hexahedral meshes in the time domain. We pay special attention to the use of Gauss-Lobatto points to perform mass lumping for any element order. We provide some theoretical results through several error estimates that are completed by various numerical experiments. c © ??? John Wile...

In this paper Gauss-Radau and Gauss-Lobatto quadrature rules are presented to evaluate the rational integrals of the element matrix for a general quadrilateral. These integrals arise in finite element formulation for second order Partial Differential Equation via Galerkin weighted residual method in closed form. Convergence to the analytical solutions and efficiency are depicted by numerical ex...

Eszter Klein’s theorem claims that among any 5 points in the plane, no three collinear, there is the vertex set of a convex quadrilateral. An application of Ramsey’s theorem then yields the classical Erdős–Szekeres theorem [19]: For every integer n ≥ 3 there is an N0 such that, among any set of N ≥ N0 points in general position in the plane, there is the vertex set of a convex n-gon. Let f(n) d...

A complete quadrilateral in the Euclidean plane is studied. The geometry of such almost as rich a triangle, so there are lot associated points, lines and conics. Hereby, study was performed rectangular coordinates, symmetrically on all four sides with parameters a, b, c, d . In this paper we will properties some circles to quadrilateral. All these well known, but here they proved by same method...

A two-phase scheme for accurate predictions of interlaminar stresses in laminated plate and shell structures has been addressed in this study. A modified superconvergent patch recovery (MSPR) technique has been utilized to obtain accurate nodal in-plane stresses which are subsequently used with the thickness integration of the three-dimensional equilibrium equations to evaluate the transverse s...

A novel node-based smoothing element for triangular and quadrilateral meshes is presented for static analysis of planar piezoelectric structures. In contrast to the smoothed finite element formulation that was based on sub-cells within an original quadrilateral element, this new method transforms a general original finite element mesh into a mesh of new smoothing cells individually associated w...