Local polynomial interpolation in a rectangle

The asymptotical error committed by approximating a smooth function by a polynomial is studied. The domain of interpolation is a rectangle in two dimensional space, and the interpolating polynomials belong to the product space of polynomials of degree at most p in one main direction and at most q in the other. For approximating polynomials we consider the use of Taylor and Lagrange interpolation polynomials. Research supported by IAN/CNR (Istituto di Analisi Numerica-CNR) grant 211.01.26, SNF (The Danisch Natural Science Research Council) grant 11-9030 (Jens Hugger) and by the U.S. Office of Naval Research grant N00014-90-J-1030 (Ivo Babuska).