【摘要】 <正> 用插值节点的均匀性,在空间中函数具有嵌入性质的条件下,导出了最佳逼近的误差估计,本文仍利用插值节点均匀性假设,对空间中的一般函数,也导出了逼近的误差估计,不再要求函数的嵌入性质; Ciarlet在仿射等价和空间函数具有嵌入性质的条件下,对一个二阶椭圆边值问题论证数值积分并不影响有限元子空间近似解逼近变分问题真解的速度。本文借助於空间中的一般函数的有限元逼近理论,对这一特殊的二阶椭圆边值问题,在基函数满足均匀性条件下,不要嵌入性质同样得到上面结果。更多还原

【Abstract】 This paper is concerned with the finite element approximation theory of the general function in Sobolev space. When the function in Sobolev space isn’t smooth enough as demanded by estimating the remainder for the Lagrange or the Hermie interpolation, one can use a modifier and the lemma of Bramble-Hilbert to get error estimates ||u-Πu||m,Ω≤chk-m|u|k,Ω in a different way. The important point in theproof of the error estimates is to prove that the interpolation operator Π u* (?)h(x)is linear continuous operator from the sobolev space Hk,2(K) into Hm,2(K)Under the condition of the affine equivalence of the elements and the smootk property of the function in sobolev space,Ciarlet[2] has proved that the numerical integration doesn’t change the rate of the convergence of the finite element approximation solution for the typical problem of the elliptic equation of second order. In this paper we don’t demand the affine equivalence of the elements and the smooth property of the function in Sobolev space.Using the similar transformation and the uniform boundary property of interpolation basic function[1] we get the above result also.更多还原