摘要
A.simplicial mesh(triangulation)is constructed that generalizes the two-dimensional 4-direction mesh to R^m.This mesh,with symmetric,shift-invariant values at the vertices,is shown to admit a bounded C^1 interpolant if and only if the alternating sum of the values at the vertices of any 1-cube is zero.This im- plies thai interpolation at the vertices of an m-dimensional,simplicial mesh by a C^1 piecewise polynomial of degree m+1 with one piece per simplex is unstable.
A.simplicial mesh(triangulation)is constructed that generalizes the two-dimensional 4-direction mesh to R^m.This mesh,with symmetric,shift-invariant values at the vertices,is shown to admit a bounded C^1 interpolant if and only if the alternating sum of the values at the vertices of any 1-cube is zero.This im- plies thai interpolation at the vertices of an m-dimensional,simplicial mesh by a C^1 piecewise polynomial of degree m+1 with one piece per simplex is unstable.
