High-order Virtual Element Method on polyhedral meshes
For computational scientists using polyhedral meshes, this provides numerical validation of high-order VEM, but the contribution is incremental as it extends known methods to 3D with numerical tests.
This paper numerically assesses the Virtual Element Method for diffusion-reaction problems on polyhedral meshes in 3D, demonstrating h-convergence for higher polynomial orders and robustness on irregular grids.
We develop a numerical assessment of the Virtual Element Method for the discretization of a diffusion-reaction model problem, for higher "polynomial" order k and three space dimensions. Although the main focus of the present study is to illustrate some h-convergence tests for different orders k, we also hint on other interesting aspects such as structured polyhedral Voronoi meshing, robustness in the presence of irregular grids, sensibility to the stabilization parameter and convergence with respect to the order k.