(untitled) (Advances in Applied Mathematics and Mechanics, 2018)
We present a proof of the discrete maximum principle (DMP) for the 1D Poisson equation −u''=f equipped with mixed Dirichlet-Neumann boundary conditions. The problem is discretized using finite elements of arbitrary lengths and polynomial degrees (hp-FEM). We show that the DMP holds on all meshes with no limitations to the sizes and polynomial degrees of the elements.