A Rational Basis for Function Approximation

TL;DR: An alternative derivation of shape functions for convex n-gons as polynomials divided by the one of n-3 is presented, which is particularly suited for large scale finite element analysis employed in the aerospace industry.

TL;DR: Numerical results show that the proposed linear strain smoothing scheme makes the approximation based on polytopes able to deliver the same optimal convergence rate as traditional quadrilateral and hexahedral approximations.

TL;DR: In this article, the divergence theorem is applied once and twice, respectively, for polygonal and polyhedral integration domains, to construct integrals on boundary wireframes, and the sum of Gaussian quadrature values on linear segments of the wireframe yields the final result of numerical integration.

TL;DR: In this paper, the authors provide a critical literature review, emphasizing on the mathematical, conceptual and implementation particularities that lead to the specific advantages and disadvantages of each method, as well as to offer numerical examples that help illustrate these features.

TL;DR: In this paper, a finite element procedure of the second order of accuracy for solving second order boundary value problems is presented and justified and numerical results are given, where the second-order boundary value problem is formulated as a set of finite element problems.