In this paper, a class of rectangular finite elements for 2m-th-oder elliptic boundary value problems in n-dimension (m,n ≥ 1) is proposed in a canonical fashion, which includes the (2m−1)-th Hermite interpolation element (n = 1), the n-linear finite element (m = 1) and the Adini element (m = 2). A nonconforming triangular finite element for the plate bending problem, with convergent order O(h)...

Article history: Received 2 October 2014 Available online 13 January 2015 Submitted by B. Kaltenbacher

Continuous extensions are now routinely provided by many IVP solvers, for graphical output, error control, or event location. Recent developments suggest that a uniform, stable and convenient interpolant may be provided directly by value and derivative data (Hermite data), because a new companion matrix for such data allows stable, robust and convenient root-finding by means of (usually built-i...

The Clifford-Hermite and the Clifford-Gegenbauer polynomials of standard Clifford analysis are generalized to the new framework of Clifford analysis in superspace in a merely symbolic way. This means that one does not a priori need an integration theory in superspace. Furthermore a lot of basic properties, such as orthogonality relations, differential equations and recursion formulae are proven...

The Hermite polynomials are simple, effective interpolants of discrete data. These interpolants can preserve local positivity, monotonicity, and convexity of the data if we restrict their derivatives to satisfy constraints at the data points. This paper describes the conditions that must be satisfied for cubic and quintic Hermite interpolants to preserve these properties when they exist in the ...