## 4 Discussion  
From the three examples, it can be seen that ADOF-FEM can achieve good results when the computational domain does or does not change with time. This is because when there is no internal heat source and the temperature of the external environment is constant, the temperature in the computational domain gradually approaches a stable value or interval over time, and the spatial distribution of temperature will gradually become gentle over time. At this point, refined mesh and more DOFs are naturally not needed to describe the drastic changes of temperature in time and space, which is the basis for the good performance of ADOF-FEM. At the same time, the transient temperature simulation during the construction of the asphalt-concrete core wall satisfies this situation approximately. Firstly, although asphalt concrete has the initial temperature of construction, there is no internal heat source. Secondly, the core wall is subjected to the thermal insulation effect of rockfill, and the surface of the core wall is affected by the external air temperature being low, due to the fact that the external environment is relatively stable. Therefore, ADOF-FEM can be used to simulate the temperature variation of the asphalt-concrete core wall during the construction period layer by layer with a coordinated mesh. Figure 15: The change of the number of DOFs and computational time in Example 3. When simulating the temperature variation of the concrete construction process or that of material adding layer by layer in additive manufacturing, the so-called zone-merged algorithm is often used. In essence, this algorithm is controlled by the user to merge multiple construction layers into one layer in a calculation step. If this kind of method is applied to the construction process of the asphalt-concrete core, it is complicated to use this method because there may be different positions in the same layer that do or do not need to be merged, and users need to preset the merging time and the merging scope. The ADOF-FEM can adaptively condense the DOFs for different positions based on the prespecified tolerance value of the judgment criterion, and it can set multiple levels of DOFs according to the number of times the mesh is refined. The different levels of DOFs can be condensed according to the judgment criteria under the same frame, so this method is simpler. It is worth noting that the prespecified tolerance value of coarsening judgment criteria is defined by users. For the asphalt-concrete core-wall dam, it has a fixed construction technology, and the temperature distribution of the different core-wall layers has common characteristics. Therefore, the temperature variation of several layers of the core-wall construction process can be pre-analyzed to obtain the appropriate prespecified tolerance value, and then the temperature of the whole core-wall dam during the construction period can be analyzed. It can be seen from the three examples that the error of the calculation results caused by ADOF-FEM at the position of master DOFs and slave DOFs is small. Compared with the temperature contour in Figures 6 and 7, using ADOF-FEM will make the smooth contour rougher in some positions, but considering that the temperature in these positions is relatively stable in time and space, such a loss of precision is acceptable. Furthermore, the computational cost saved by ADOF-FEM is mainly the two parts of matrix factorization and solving the equation in FEM because the time spent in these two parts is directly related to the number of DOFs. However, the total computational time also includes assembling the global conductivity matrix, which is related to the number of elements, and ADOF-FEM itself cannot reduce the number of elements in the computational mesh, so it cannot save this part of computational time. Therefore, there is an upper limit in using ADOF-FEM to save the computational cost.