特征值问题的非协调元逼近

本文给出了双调和方程特征值问题的非协调元逼近,得出了与[1]、[2]中利用协调元时完全相同的收速估计.

一类四阶Sigroniri型问题的非协调元逼近

本文以Morely元为例,研究了一个由一类四阶Sigroniri型问题引起的四阶变分不等式的非协调元逼近,导出了近似解的误差估计。

非线性Sine-Gordon方程的一个新非协调混合元格式

针对非线性sine-Gordon方程利用EQrot1和零阶Raviart-Thomas元建立一个自然满足Brezzi-Babuka条件的新非协调混合元逼近格式.基于EQrot1非协调元的两个特殊性质:(i)当精确解属于H3(Ω)时,其相容误差为O(h2)阶,比它的插值误差O(h)高一阶;(ii)插值算子与Riesz投影算子等价,再结合零阶Raviart-Thomas元的高精度分析结果和插值后处理技术,针对半离散逼近格式导出原始变量u和流量p分别在H1模和L2模意义下的超逼近性及超收敛结果.同时,对于提出的一个具有二阶精度全离散逼近格式,得到相应的最优误差估计.

位移障碍下一个四阶变分不等式的某些强间断非协调元逼近

考虑[1]中四阶变分不等式问题:其中为非空闭凸集,而障碍函数φ∈C^2(Ω),φ<0,在?Ω上.关于解的性质,有下述结果:当Ω?R^2是具有光滑边界?Ω的有界凸区域且f∈L^2(Ω)时,问题(1)

A class of nonconforming quadrilateral finite elements for incompressible flow

This paper focuses on the low-order nonconforming rectangular and quadrilateral finite elements approximation of incompressible flow.Beyond the previous research works,we propose a general strategy to construct the basis functions.Under several specific constraints,the optimal error estimates are obtained,i.e.,the first order accuracy of the velocities in H1-norm and the pressure in L2-norm,as well as the second order accuracy of the velocities in L2-norm.Besides,we clarify the differences between rectangular and quadrilateral finite element approximation.In addition,we give several examples to verify the validity of our error estimates.