In simulation of heat conduction with temperature-independent physical properties and boundary conditions (BCs), Galerkin residual analysis and variational analysis yield equivalent finite element method (FEM), the conventional FEM. However, if the properties and BCs are temperature-dependent, it is discovered that their derivatives further induce nonlinearity of FEM which consequently generates divergence between the two analyses. A general FEM, extension of variational analysis, is derived as general form of conventional FEM modeling nonlinear heat conduction. Numerical examples demonstrate that the general FEM produces results with considerably higher accuracy and stability and also possesses higher performances on conforming with both two analyses. Since general FEM degenerates to conventional FEM if derivatives are of small-amplitude or zero and its direct implementation to the entire domain is costive, general FEM is alternatively utilized as local refinement of governing equation only to points with significant derivatives. The strategy of local refinement is optimized to enhance efficiency.

在具有与温度无关的物理属性和边界条件 (BC) 的热传导模拟中，Galerkin 残差分析和变分分析产生等效有限元方法 (FEM)，即传统的 FEM。然而，如果属性和 BC 与温度有关，则发现它们的导数会进一步引起 FEM 的非线性，从而在两种分析之间产生分歧。通用 FEM，变分分析的扩展，是作为常规 FEM 建模非线性热传导的一般形式导出的。数值例子表明，通用有限元法产生的结果具有更高的准确性和稳定性，并且在符合两种分析方面也具有更高的性能。由于如果导数为小幅值或零，一般 FEM 退化为传统 FEM，并且其对整个域的直接实现成本高昂，因此一般 FEM 可替代地用作仅对具有显着导数的点的控制方程的局部细化。优化局部细化策略，提升效率。