Interpolation theory of anisotropic finite elements and applications (Q2519301)

The authors provide us with a new technique to analyze the interpolation error of anisotropic finite element methods. In their technique, the interpolation error is obtained thanks to the use of the Newton's formula of the interpolation polynomials on the reference element. The error interpolation on a general element could be obtained, as usual thanks to transformation inequalities of function semi norms between a general element and the reference element. These interpolation errors are used by the authors to derive some error estimates of anisotropic finite element methods.