𝔖 Bobbio Scriptorium
✦   LIBER   ✦

C1 quadratic macroelements and C1 orthogonal multiresolution analyses in 2D

✍ Scribed by Tian-Xiao He

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
593 KB
Volume
40
Category
Article
ISSN
0898-1221

No coin nor oath required. For personal study only.

✦ Synopsis

Each triangle of an arbitrary regular triangulation A of a polygonal region f~ in R 2 is subdivided into twelve subtriangles by using three connecting lines joining three arbitrarily chosen points on its edges, three connecting lines from an arbitrarily chosen interior point in the triangle to its three vertices, and three connecting lines joining the points on the edges and the interior point. In this refinement /k of A, C 1 quadratic finite elements can be constructed. In this paper, we will give explicit B~ier coefficients of elements in terms of the parameters that describe function and first partial derivative values at vertices and values of the normal derivatives at vertices of subtriangles that lie on the edges of A. Consequently, the basis and approximation properties of C 1 quadratic spline space under refined grid partition/k can be found. Finally, we discuss the construction of C 1 orthogonal scaling functions by using C 1 quadratic macroelements.

πŸ“œ SIMILAR VOLUMES

Global minimum and orthogonality in C1-c
Global minimum and orthogonality in C1-classes
✍ Salah Mecheri; Messaoud Bounkhel πŸ“‚ Article πŸ“… 2003 πŸ› Elsevier Science 🌐 English βš– 187 KB

In this paper we characterize the global minimum of an arbitrary function defined on a Banach space, in terms of a new concept of derivatives adapted for our case from a recent work due to D.J. Keckic (J. Operator Theory, submitted for publication). Using these results we establish several new chara