Consider approximants over conforming (or face-to-face) meshes that are generated by means of bisection of simplices. Then the tree approximation algorithms by Binev and DeVore (2004) and Binev (2018) construct near best approximants with quasi-optimal complexity. Doing so, the decisions in the algorithm do not take into account the requirement of conformity. This entails that the near best constant depends on the completion process which turns a nonconforming mesh into a conforming one.

We shall generalize the tree approximation algorithm form Binev (2018) to take into account the conformity of the generated meshes, thereby avoiding the aforementioned dependence.