Anisotropic spline approximation with non-uniform B-splines

Recently the author and U. Reif introduced the concept of diversification of uniform tensor product B-splines. Based on this concept, we give a new constructive modification of non-uniform B-splines. The resulting spline spaces are perfectly fitted for the approximation of functions defined on domains Omega subset of R-2. We build a bounded quasi-interpolant and prove that for our spline spaces an anisotropic error estimate in the Lp-norm, 1 <= p <= infinity, is valid. In particular, we show that the constant of the error estimate does not depend on the shape of Omega or the knot grid.