DIV - CURL Vector Quasi - interpolation on a Finite

| This paper presents a quasi-interpolation method for DIV-CURL vector splines in two dimensions on both innnite and nite domains. The quasi-interpolant is a linear combination of translates of dilates of a basis function. In particular, our discussion focuses on the approximation of a vector-valued function deened on a nite domain for practical application purposes. In such a case, edge functions are introduced for preserving the convergence of the quasi-interpolant on the boundaries. These edge functions can be determined by means of the polynomial reproduction properties of the quasi-interpolation. The analysis of convergence has shown that the quasi-interpolant deened on a regular grid of whole R 2 can reproduce linear polynomial and has an O(h 2 j log hj) error bound, while the modiied quasi-interpolant deened on a square I 2 has an O(h) error bound if the edge functions are designed for reproducing a constant.