The boundaries of a rectangle (size 1 by 1) have prescribed temperature 0.
The middle point is heated so that it gets temperature 1. The residual remeshing is used to capture the temperature distribution near the heated spot in the middle. After some time, the temperature in the middle is imposed, and the residual remeshing did locate nodes more closely to the middle. The number of nodes is not changed; the nodes are replaced in the direction of high equation residual.