L_2投影与Galerkin投影的渐近展开

本文在等距三角剖分以及线性有限元函数空间的条件下,给出了已知函数的L_2投影及Galerkjn投影的以线性插值为主项的渐近展开式。应用于抛物问题,得到了半离散抛物问题Galerkjn解的渐近展开式。

On Asymptotic Expansions of L_2 Projection and Galerkin Projection

The purpose of this paper is to provide asymptotic expansions for the linear finite element solutions of elliptic and parabolic equations. Under condition that the trangulations are regular, we derive firstly expansion formulae with linear interpolations as their principle parts for the L_2 projection and the Galerkin projection of Poissons equation. Moreover, as an application, similar asymptotic expansion also proved for the semidiscrete finite element solution of heat equation by the help of semigroop theory.