Bidimensional interpolation operators of finite element type and degree of exactness two

Abstract

For a given arbitrary triangulation of \(\mathbb R^2\), we construct an interpolating operator which is exact for the polynomials in two variables of total degree \(\leq 2\). This operator is local, in the sense that the information around an interpolation node is taken from a small region around this point. We study the remainder of the interpolation formula.

Keywords

• two-dimensional interpolation operator
• degree of exactness