Explicit Estimation Of Interpolation Error In Sobolev Space And Its Application In Finite Element

In this paper, we mainly study the way of the explicit estimation for the piecewise linear interpolation function in Sobolev Space. By means of the Taylor expansion of the exact solution, we obtain an explicit and maneuverability method for settling the corresponding problems. In particular, the specific error constants of several common estimations of the interpolation error are given. Meanwhile, we explicitly obtain the error constants of the error estimate without the regular assumption and the explicit estimation of the special non-conforming element. Such highly accurate approximate values can be widely used for a priori and a posterior error estimations in adaptive computation and numericial verification of the finite element solutions.