王红（1994—），女，硕士（E-mail: [email protected]）；李小林（1983—），男，教授（通讯作者. E-mail: [email protected]）.

中图分类号: O241.82 采用无单元Galerkin(element-free Galerkin，EFG)法求解具有混合边界条件的二维瞬态热传导问题.首先采用二阶向后微分公式离散热传导方程的时间变量，将该问题转化为与时间无关的混合边值问题；然后采用罚函数法处理Dirichlet边界条件，建立了二维瞬态热传导问题的无单元Galerkin法；最后基于移动最小二乘近似的误差结果，详细推导了无单元Galerkin法求解二维瞬态热传导问题的误差估计公式.给出的数值算例表明计算结果与解析解或已有数值解吻合较好，该方法具有较高的计算精度和较好的收敛性. 二维瞬态热传导问题 无单元Galerkin法 二阶BDF格式 Abstract: The element-free Galerkin (EFG) method was introduced to solve 2D transient heat conduction problems. Firstly, with the 2nd-order BDF scheme to address the time derivative term, the original problem was transformed into a series of time-independent mixed boundary value problems. Then, the penalty method was adopted to treat the Dirichlet boundary condition, and the element-free Galerkin method was established for 2D transient heat conduction problems. Finally, based on the error results of the moving least squares approximation, the error estimation of the element-free Galerkin method for 2D transient heat conduction problems was derived in detail. Numerical examples show that, the calculation results are in good agreement with the analytical solutions or the existing numerical solutions, and the EFG method has higher calculation accuracy and better convergence. Key words: 2D transient heat conduction problem element-free Galerkin method 2nd-order BDF scheme error estimation