Weakened acute type condition for tetrahedral triangulations and the discrete maximum principle

Abstract

We prove that a discrete maximum principle holds for continuous piecewise linear finite element approximations for the Poisson equation with the Dirichlet boundary condition also under a condition of the existence of some obtuse internal angles between faces of terahedra of triangulations of a given space domain. This result represents a weakened form of the acute type condition for the three-dimensional case.