一个二阶椭圆混合问题的三棱柱元

A Triangular Prism Finite Element for the Second-Order Elliptic Mixed Problem

二阶椭圆混合问题的有限元方法已有很多研究,包括三角形元、矩形元、四面体元和立方体元.但对三棱柱元的研究却很少,三棱柱元兼顾三角形和矩形的优点,更加适合柱形区域,尤其是截面复杂的柱形区域.该文对二阶椭圆混合问题构造一个低阶的三棱柱元,证明了它的适定性和收敛性,给出了最优的误差估计.

There are many researches on the finite element method for second-order elliptic mixed problem,including triangular element,rectangular element,tetrahedral element and cubic element.However,there are few researches on the triangular prism element.The triangular prism element has the advantages of triangular and rectangular elements,and it is more suitable for cylindrical region,especially for the cylindrical region with complex cross-section.In this paper,a lower-order conforming triangular prism element is constructed for the second-order elliptic mixed problem.Its well-posedness and convergence are proved,and the optimal error estimate is given too.