\(C^1\) quadratic macroelements and \(C^1\) orthogonal multiresolution analyses in 2D
The author presents a way to divide a triangle of an arbitrary regular triangulation \(\Delta\) of a polygon region in \(R^{2}\) into twelve subtriangles. In this refinement \(C^{1}\) quadratic finite elements can be constructed. The paper gives explicit Bézier 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 \(\Delta\). The basis and approximation properties of the \(C^{1}\) quadratic spline space under the refined grid partition are found. Finally, the construction of \(C^{1}\) orthogonal scaling functions by using \(C^{1}\) quadratic macroelements is discussed.
\(C^{1}\) orthogonal multiresolution analysis
scientific article; zbMATH DE number 1471519