【摘要】 <正> 1引 言 有限元超收敛的研究已有二、三十年的历史,经过众多学者的努力,取得了丰硕的成果.有多部专著问世,国内的有[1],[2],[3]等,国外的则有[4].有限元超收敛一般对网格有一定的限制要求.对于三角形网格,要求满足C条件,PC条件或6PC条件(见[1]).C条件要求任意两个相邻三角形单元近似构成一平行四边形,其实质是任意单元的三条更多还原

【Abstract】 In this paper, superconvergence of the lowest order Raviart-Thomas mixed finite element approximation for second order Neumann boundary value problem on fishbone shape meshes is analyzed. The main term of the error between the exact solution and the finite element interpolating function is determined by Bramble-Hilbert lemma on the individual finite element. A part of the main term of the error on two adjacent finite elements can be cancelled along the special direction, and thus the higher order error estimate is obtained on the whole domain by summation. Compared with the general finite element error estimate, the convergence rate can be increased from order one to order two in L2-norm by postprocessing superconvergence technique.更多还原