Local Lagrange interpolation by quintic \(C^1\) splines on type-6 tetrahedral partitions
Piecewise polynomial splines in three dimensions are defined with which interpolation can be carried out. The splines are of degree five and defined on tetrahedra. The individual polynomial pieces are joined so that the complete spline is differentiable. The interpolation is of Lagrange type and the authors show existence and uniqueness for the interpolants for the given data. As a consequence, the interpolation scheme is local and has linear complexity. They also show stability and include an approximation order theorem. The latter bounds the uniform error on a compact polyhedral domain by a multiple of \(h^{m+1}\), where \(h\) is the length of the edges of the cube partition and \(m\) is at most five. Further, derivatives of the approximation error are bounded, too.
scientific article; zbMATH DE number 5987773