A simple Hessian-based 3D mesh adaptation technique with applications to the multigroup diffusion equations

A simple error estimation and mesh adaptation procedure is proposed for the multigroup multi-dimensional diffusion equations. The procedure estimates the values of the second-order derivatives of the current numerical solution to drive the mesh refinement. Different spatial meshes are obtained for each component of the multigroup flux in order to follow the physics appropriately. This requires the proper handling of the group coupling terms arising in the multigroup diffusion equations. Results are presented in 2D and 3D.