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

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