Discrete maximum principle for FE solutions of the diffusion-reaction problem on prismatic meshes (Q1008695)

The authors consider the discrete maximum principle (DMP) for a stationary three-dimensional diffusion-reaction problem solved by means of prismatic finite elements (FEs). They derive geometric conditions on the shape parameters of the prismatic partitions which guarantee validity of the DMP a priori. The main result of this paper is a theorem where an ``easily verifiable condition'' is presented in order to guarantee the DMP. The authors also present numerical tests to show the sharpness of the theoretically obtained conditions.