In this paper,a nonconforming rectangular plate element,the modified incomplete biquadratic plate element,is considered. The asympotic optimal L~∞-error estimate is obtained for the plate bending problem. This proof ...In this paper,a nonconforming rectangular plate element,the modified incomplete biquadratic plate element,is considered. The asympotic optimal L~∞-error estimate is obtained for the plate bending problem. This proof is based on the method of regularized Green's function and 'the trick of auxiliary element'.展开更多
The paper studies the convergence and the superconvergence of the biquadratic finite element for Poisson＇ problem on anisotropic meshes. By detailed analysis, it shows that the biquadratic finite element is anisotrop...The paper studies the convergence and the superconvergence of the biquadratic finite element for Poisson＇ problem on anisotropic meshes. By detailed analysis, it shows that the biquadratic finite element is anisotropically superconvergent at four Gauss points in the element. Key words：展开更多
基于双二次元及其梯度空间,建立了抛物型积分微分方程的一种新混合有限元逼近格式.在不需要Ritz-Volterra投影的前提下,直接利用双二次元插值的高精度结果及关于时间变量的导数转移技巧,在半离散格式下,得到了原始变量u和中间变量p=▽u+...基于双二次元及其梯度空间,建立了抛物型积分微分方程的一种新混合有限元逼近格式.在不需要Ritz-Volterra投影的前提下,直接利用双二次元插值的高精度结果及关于时间变量的导数转移技巧,在半离散格式下,得到了原始变量u和中间变量p=▽u+integral from n=0 to t▽u(s)ds分别关于H^1模和L^2模的O(h^4)阶超逼近结果,相比插值误差估计,提高了二阶精度.与此同时,对向后Euler格式,导出了u和p分别在H^1模与L^2模意义下的O(h^4+τ)阶超逼近;对Crank-Nicolson-Galerkin格式,在L^2模意义下证明了u和p分别具有O(h^4+τ~2)和O(h^3+τ~2)阶的超逼近性质.其中,h,τ分别表示空间剖分参数和时间步长,t代表时间变量.展开更多
文摘In this paper,a nonconforming rectangular plate element,the modified incomplete biquadratic plate element,is considered. The asympotic optimal L~∞-error estimate is obtained for the plate bending problem. This proof is based on the method of regularized Green's function and 'the trick of auxiliary element'.
基金the Henan Natural Science Foundation(072300410320)the Foundation Study of the Education Department of Henan Province(200510460311)
文摘The paper studies the convergence and the superconvergence of the biquadratic finite element for Poisson＇ problem on anisotropic meshes. By detailed analysis, it shows that the biquadratic finite element is anisotropically superconvergent at four Gauss points in the element. Key words：
文摘基于双二次元及其梯度空间,建立了抛物型积分微分方程的一种新混合有限元逼近格式.在不需要Ritz-Volterra投影的前提下,直接利用双二次元插值的高精度结果及关于时间变量的导数转移技巧,在半离散格式下,得到了原始变量u和中间变量p=▽u+integral from n=0 to t▽u(s)ds分别关于H^1模和L^2模的O(h^4)阶超逼近结果,相比插值误差估计,提高了二阶精度.与此同时,对向后Euler格式,导出了u和p分别在H^1模与L^2模意义下的O(h^4+τ)阶超逼近;对Crank-Nicolson-Galerkin格式,在L^2模意义下证明了u和p分别具有O(h^4+τ~2)和O(h^3+τ~2)阶的超逼近性质.其中,h,τ分别表示空间剖分参数和时间步长,t代表时间变量.
