Finite Element Approximation of a Nonlinear Steady-State Heat Conduction Problem (Journal of Computational Mathematics, 2001)
We examine a nonlinear partial differential equation of elliptic type with the homogeneous Dirichlet boundary conditions. We prove comparison and maximum principles. For associated finite element approximations we introduce a discrete analogue of the maximum principle for linear elements, which is based on nonobtuse tetrahedral partitions.