Near-Best Adaptive Approximation on Conforming Meshes

We devise a generalization of tree approximation that generates conforming meshes, i.e., meshes with a particular structure like edge-to-edge triangulations. A key feature of this generalization is that the choices of the cells to be subdivided are affected by that particular structure. As main result, we prove near best approximation with respect to conforming meshes, independent of constants such as the completion constant for newest-vertex bisection. Numerical experiments complement the theoretical results.