Finite element multiwavelets

Finite elements with support on two intervals span the space of piecewise polynomials with degree 2n-1 and n-1 continuous derivatives. Function values and n-1 derivatives at each mesh-point determine these “Hermite finite elements”. The n basis functions satisfy a dilation equation with n by n matrix coefficients. Orthogonal to this scaling subspace is a wavelet subspace. It is spanned by the translates of n wavelets W_i(t), each supported on three intervals. The wavelets are orthogonal to all rescalings W_i(2⁰t-k), but not to translates at the same level (j=0). These new multiwavelets achieve 2n vanishing moments and high regularity with symmetry and short support