An element decomposition method for heat transfer analysis

In this work, an element decomposition method (EDM) is formulated to deal with heat transfer analysis. For this method, the quadrilateral elements are first divided into sub-triangular cells and the local temperature gradient in each sub-triangular cell is obtained using linear interpolation function. Then, the temperature gradient of whole quadrilateral can be calculated by averaging the local gradient in each sub-domain. As only one integration point is utilized for each element, the computational cost of presented method is much less and no mapping or coordinate transformation is involved. Several numerical examples are given to fully test the validity of this method and it is found that the EDM is very accurate, stable and can achieve high level of convergence when solving heat transfer problems.