一维问题有限元的超收敛性质

对一维投影型插值算子和两点边值问题的有限元近似,证明了剖分单元上的Ｌｏｂａｔｏ点、Ｇａｕｓ点和拟Ｌｏｂａｔｏ点分别是函数、一阶和二阶导数逼近的超收敛点,并且在两点算术平均意义下,导出了函数和各阶导数逼近的强超收敛性,即比整体最优收敛阶高出二阶的超收敛性·

On Superconvergence Properties for Finite Element Approximations in One Dimensional Space

For the interpolating operator of projection type and the finite element approximations of two point boundary value problems,it is shown that the Lobatto,Gauss and quasi Lobatto points on each subdivision element are superconvergence points for function,one order and two order derivative approximations,respectively.And under two point arithmetic mean,these approximations possess ultraconvergence property which imply the convergence rates are two orders higher than the optimal global convergence rates.