组合杂交三角形单元的加权能量正交关系

组合变分原理可以增强杂交元方法解的稳定性。建立热传导方程基于区域分解的组合杂交有限元方法,给出单元上温度梯度插值为线性、但温度插值为协调线性插值与非协调二次插值之和的组合杂交三角形单元,并通过数值实验验证理论结果的正确性。结果表明:分片线性温度梯度插值的散度(热源)与非协调温度插值是加权能量正交的;组合杂交三角形元刚度矩阵等同于协调的三角形线性元刚度矩阵,即非协调部分无温度增强特性。

The weighted energy orthogonal relation of combined hybrid triangular element

Combined variation principles can enhance the stability of numerical solution, combined hybrid finite element method of heat transfer equation is built on the basis of the domain decomposition technique. The combined hybrid triangular element, in which the temperature gradient is interpolated by linear polynomials on each element, but the temperature is interpolated by the sum of the linear polynomials and the non-conforming quadratic polynomials, is given. Unlike the combined hybrid rectangular element, only the weighted energy orthogonal relation of the divergence of piecewise linear temperature gradient interpolation and the non-conforming temperature interpolation is given. The stiffness matrix of this element of is equivalent to the conforming triangular linear element, and the non-conforming parts have no contribution to temperature evaluation. At last, the numerical experiments verify the accuracy of the theoretical results.