Mesh adaptation and optimization for discontinuous galerkin methods using a continuous mesh model
We present a method for anisotropic mesh adaptation and optimization for high-order Discontinuous Galerkin (DG) Schemes. Given the total number of degrees of freedom, we propose a metric-based method, which aims to globally optimize the mesh with respect to the Lq norm of the error. This is done by minimizing a suitable error model associated with the approximation space. Advantages of using a metric based method in this context are several. Firstly, it facilitates changing and manipulating the mesh in a general nonisotropic way. Secondly, defining a suitable continuous interpolation operator allows us to use an analytic optimization framework which operates on the metric field, rather than the discrete mesh. We present the formulation of the method as well as numerical experiments in the context of convection-diffusion systems.
