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C1 Quadratic Macroelements and C1 Orthogonal Multiresolution Analyses in 2D
Computers and Mathematics with Applications (2000)
  • Tian-Xiao He, Illinois Wesleyan University
Abstract

Each triangle of an arbitrary regular triangulation Δ of a polygonal region in R2 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, C1 quadratic finite elements can be constructed. In this paper, we will give explicit Bezier 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 Δ. Consequently, the basis and approximation properties of C1 quadratic spline space under refined grid partition Δ can be found. Finally, we discuss the construction of C1 orthogonal scaling functions by using C1 quadratic macroelements.

Publication Date
2000
Citation Information
Tian-Xiao He. "C1 Quadratic Macroelements and C1 Orthogonal Multiresolution Analyses in 2D" Computers and Mathematics with Applications Vol. 40 (2000)
Available at: http://works.bepress.com/tian_xiao_he/33/