Lagrange interpolation set along linear piecewise algebraic curves

Abstract

Abstract. This paper discusses the Lagrange interpolation problem in continuous bivariate spline spaces over regular triangulations. By using the so-called Lagrange interpolation set along piecewise algebraic curves, we develop a new approach of constructing the interpolation set for continuous spline spaces. We show the property of this set on star region, and construct the interpolation set for continuous bivariate spline spaces over arbitrary triangulations. The construction only depends on the number of points on the piecewise algebraic curve in each cell.