Interpolation Hermite Polynomials For Finite Element Method

Abstract

Abstract. We describe a new algorithm for analytic calculation of high-order Hermite interpolation polynomials of the simplex and give their classification. A typical example of triangle element, to be built in high accuracy finite element schemes, is given.

Hermite Numerical Method to Estimate the Radon and Radium Effects of the Soil in Bartella Region

“…Recently, many researcher have been studied the estimation subject as, the finite element method (FEM) which is an efficient method for solving the engineering and mathematical physics most diverse problems [6]. The absorbed dose estimation of surface skin for the standard radiological examinations of the patient [7].…”

High-Accuracy Finite Element Method: Benchmark Calculations

“…The polyhedral domain Ω = Ω h (z) = Q q=1 ∆ q is divided in finite elements in the form of simplexes ∆ q with HIPs or LIPs ϕ κ r (z), calculated using the Algorithm of [1]. The piecewise polynomial functions P l (z) of the order p with continuous derivatives to the order κ are constructed by joining the polynomials ϕ …”

“…The eigenvalues of this problem having degenerate spectrum are the integers E m = m Table 1 of paper [1], conserving the continuity of the first and the second derivative of the approximate solution, respectively. As seen from Fig.…”

“…[1] we present a new algorithm for the calculation of high-order Lagrange and Hermite interpolation polynomials (LIP and HIP) of the simplex in analytical form, their classification and a typical example of the triangle element for high-accuracy finite element method (FEM) schemes. In this paper we show the efficiency of the schemes using high-order accuracy LIP and HIP for benchmark calculations of the exactly solvable problems for the triangle membrane and hypercube.…”

Construction of Multivariate Interpolation Hermite Polynomials for Finite Element Method

“…In recent decade we presented a new algorithm for the calculation of high-order Lagrange and Hermite interpolation polynomials (LIP and HIP) [1] of the simplex in analytical form, their classification and a typical example of the triangle element for high-accuracy finite element method (FEM) schemes [2][3][4]. We have illustrated the efficiency of the schemes using high-order accuracy LIP and HIP on benchmark calculations of exactly solvable boundary value problems(BVPs)for a triangle membrane, a hypercube and a helium atom [5,6].…”