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In order to cure the instability of NS-FEM and further improve the accuracy, a stable node-based smoothed finite element method (SNS-FEM) is formulated for steady and transient heat transfer problems using linear triangular and tetrahedron element. In present method, both smoothed temperature gradient and variance of temperature gradient in smoothing domains are considered. The accuracy, computational efficiency and stability of SNS-FEM are examined through several numerical examples with different kinds of boundary conditions. It is found that present method is more accurate and efficient than traditional finite element method (FEM) and NS-FEM. Most importantly, compared with NS-FEM, present SNS-FEM can be very stable when dealing with transient heat transfer problems.

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