In the error analysis of the finite elements, there appear various positive constants. In general, we can prove the existence of the error constants and their independence of element size, but not give the concrete expressions and some upper bounds. It is very helpful for the practical engineering computation to evaluate or bound the constants, which is the explicit error estimation. In this paper, by using Poincare inequality and some basic properties of divided difference, we explicitly estimate the Lagrange interpola-tion error and further give anisotropic error estimates in various norms (or semi-norms) based on Newton’s formula of polynomial interpolation. Furthermore, we discuss the explicit error estimation for general finite elements and anisotropic interpolations, and give the relevant results. Such explicit error estimates can be used as computable error bounds in adaptive computation of finite element solutions. |