DISCRETE MAXIMUM PRINCIPLE FOR PRISMATIC FINITE ELEMENTS

The paper deals with a diffusion-reaction problem with homogeneous Dirichlet boundary conditions and presents conditions for the prismatic finite element meshes which guarantee the validity of the corresponding discrete maximum principle (DMP). These conditions are easy to verify and they imply a sufficient and a necessary bound to the maximal angle alpha((T))(max) in the triangular base T of a prism. The sufficient condition is alpha((T))(max) <= arctan root 7 and the necessary condition is alpha((T))(max) <= arctan root 8. If the maximal angle is in between these two values then the other angles in the triangle play a role.