椭圆问题中一种联合NC1-C2方法的分析
Analysis of a combined NC1-C2 method for elliptic problem
AI总结：
本文提出一种结合NC1和C2的有限元方法，用于求解椭圆问题，通过理论分析和数值实验验证了其有效性与稳定性。
摘要：
本文展示了一种使用P¹非协调多项式和P²协调多项式的非协调有限元方法，能够简便地构建和应用。该方法是标准分段二次六节点元素的'增强'版本。本文分为两部分：第一部分介绍了该元的基性质，包括其构建方法和基本误差估计；我们观察到该新元行为类似于P¹非协调元。第二部分将该元应用于椭圆问题，理论估计通过数值结果得到保证。
英文摘要：
It is shown in this paper that non-conforming finite elements on the triangle using $P^{1}$-nonconforming polynomials and $P^{2}$ -conforming polynomials can be easily built and used.They appear as an 'enriched' version of the standard piecewise quadratic six-node element.This work is divided into two parts.In the first we present the basic- property of the element,namely how it can be built and basic error estimates.We have observed that this new element behaves like $P^{1}$ non-conforming element.In the second part we have applied our element to the elliptic problem and the theoretical estimate has been guaranteed by numerical result.
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