A continuous-mesh optimization technique for piecewise polynomial approximation on tetrahedral grids
Abstract
Building on previous research we present a three-dimensional formulation of a metricbased mesh optimization scheme. The intended application area is higher order (discontinuous) Galerkin schemes for convection-diffusion problems.
Ultimately, as in our previous two-dimensional formulation, the aim is to use the method for compressible flow simulation. Similar to the two-dimensional formulation, we combine a local (analytical) optimization of the anisotropy with an ensuing global optimization of the mesh density distribution.
In particular the local optimization of the mesh anisotropy is a non-trivial extension of the two-dimensional case. Both optimization steps are built on a suitable continuous-mesh error estimate.
The scheme is parameter-free, using only the total integrated mesh density as a constraint. We present the derivation of the method, as well as numerical experiments using model problems.