Lagrange and average interpolation over 3D anisotropic elements

On the Average Errors of Multivariate Lagrange Interpolation

On Multivariate Lagrange Interpolation

Lagrange interpolation by polynomials in several variables is studied through a finite difference approach. We establish an interpolation formula analogous to that of Newton and a remainder formula, both of them in terms of finite differences. We prove that the finite difference admits an integral representation involving simplex spline functions. In particular, this provides a remainder formul...

Barycentric Lagrange Interpolation

Barycentric interpolation is a variant of Lagrange polynomial interpolation that is fast and stable. It deserves to be known as the standard method of polynomial interpolation.

Stieltjes polynomials and Lagrange interpolation

Bounds are proved for the Stieltjes polynomial En+1, and lower bounds are proved for the distances of consecutive zeros of the Stieltjes polynomials and the Legendre polynomials Pn. This sharpens a known interlacing result of Szegö. As a byproduct, bounds are obtained for the Geronimus polynomials Gn. Applying these results, convergence theorems are proved for the Lagrange interpolation process...

Interpolation Error Estimates for Edge Elements on Anisotropic Meshes

The classical error analysis for the Nédélec edge interpolation requires the so-called regularity assumption on the elements. However, in [18], optimal error estimates were obtained for the lowest order case, under the weaker hypothesis of the maximum angle condition. This assumption allows for anisotropic meshes that become useful, for example, for the approximation of solutions with edge sing...