New Discretization Methodology on Polyhedral Meshes

Franco Brezzi brezzi@cut.this.part.imati.cnr.it

Konstantin Lipnikov lipnikov@cut.this.part.lanl.gov

Mikhail Shashkov shashkov@cut.this.part.lanl.gov

Nowadays, a growing number of complex engineering simulations shows advantage of using polyhedral meshes. Unfortunately, most of the existing numerical methods cannot be extended to polyhedral meshes, especially to meshes with cells having strongly curved (non-planar) faces. For a diffusion problem, we developed a new discretization methodology that overcomes this problem.