A comparative numerical study of meshing functionals for variational mesh adaptation
For researchers in computational mesh generation, this provides a numerical comparison of existing functionals, but the results are incremental and lack concrete performance numbers.
The study compares three mesh adaptation functionals (Winslow's variable diffusion, equidistribution-based, and alignment-based) in 2D and 3D, evaluating their performance using equidistribution and alignment quality measures.
We present a comparative numerical study for three functionals used for variational mesh adaptation. One of them is a generalisation of Winslow's variable diffusion functional while the others are based on equidistribution and alignment. These functionals are known to have nice theoretical properties and work well for most mesh adaptation problems either as a stand-alone variational method or combined within the moving mesh framework. Their performance is investigated numerically in terms of equidistribution and alignment mesh quality measures. Numerical results in 2D and 3D are presented.