Some definitions on stability of interpolating process are given and then the sufficient and necessary conditions are obtained. On this basis, we conclude that the Lagrange interpolation is unstable, ...

General aspects of polynomial interpolation theory. Formulations in different basis, e.g. Lagrange, Newton etc. and their approximation and computational properties ...

The finite element method with an arbitrary mesh gives only a lower order convergence (even if the exact solution is smooth). By using the (nearly) rectangular meshes and combining with an ...