组合杂交Wilson矩形单元的加权能量正交关系  

The weighted energy orthogonal relation of combined hybrid Wilson rectangular element

作　　者：聂玉峰[1] 张玲[1] 王惠玲[1] 

机构地区：[1]西北工业大学应用数学系,陕西西安710129

出　　处：《陕西师范大学学报（自然科学版）》2014年第6期26-30,共5页Journal of Shaanxi Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11471262)

摘　　要：为增强杂交元方法解的稳定性,建立了热传导方程的基于区域分解的组合杂交有限元方法,给出了单元上温度梯度插值为线性、但温度插值为协调双线性插值与Wilson非协调二次插值之和的组合杂交矩形单元.不同于对弹性力学问题的求解,非协调温度插值的梯度(热流)与分片线性温度梯度插值加权能量正交,并且分片线性温度梯度插值的散度(热源)与非协调温度插值加权能量正交.组合杂交矩形元刚度矩阵等同于协调的矩形双线性元刚度矩阵,即非协调部分无温度增强特性.For the enhanced stability of numerical solution,combined hybrid finite element meth-od of heat transfer equation is built based on domain decomposition technique.The combined hy-brid rectangular element,in which the temperature gradient is interpolated by linear polynomials on each element,but the temperature is interpolated by the sum of the bilinear polynomials and the Wilson non-conforming quadratic polynomials is given.Unlike in the case of elasticity prob-lem,the weighted energy orthogonal relations between the gradient of non-conforming tempera-ture interpolation and piecewise linear temperature gradient interpolation as well as the divergence of piecewise linear temperature gradient interpolation and the non-conforming temperature inter-polation are given respectively.This element of stiffness matrix is equivalent to the conforming rectangular bilinear element,and the non-conforming parts have no contribution to temperature e-valuation.

关 键 词：组合稳定 能量正交 温度增强 刚度矩阵 

分 类 号：O242.21[理学—计算数学]