Anisotropic Mesh Adaptation Method, hp-Variant

We present an hp-variant of the anisotropic mesh adaptation methods discussed so far. That is, contrary to our discussion in Chap. 5, we now let the polynomial degree of approximation vary from mesh element to mesh element. This is essential in situations where the exact solution contains local singularities but is very smooth in other parts of the computational domain. The main concern here is the extension of the continuous mesh and error models to the hp-variant. However, as the analytical solution of the pertinent optimization problem is not as straightforward as in the h-variant, we derive a semi-analytical iterative approach.

Duke Scholars

Author Georg May DKU Faculty