Triangular wavelet based finite elements via multivalued scaling equations Original Research Article

This paper develops a class of triangular finite elements based on L2(Rn) orthonormal compactly supported wavelets. As in the case of recently derived tensor product wavelet elements, the triangular elements are defined by deriving an algebraic eigenvalue problem characterizing the entries of the elemental matrices. These entries are uniquely defined by normalization conditions derived from the polynomial reproducing properties of the wavelet scaling functions. The work herein generalizes the development of the tensor-product wavelet elements in that the geometry of the triangular elemental domain is characterized using a multivalued scaling equation. The multivalued scaling function is used to represent the self-similar tiling of Rn onto itself by triangular domains.