  The maximum principle forms an important qualitative property of second order
elliptic equations, therefore its discrete analogues, the so-called discrete
maximum principles (DMPs) have drawn much attention. In this paper DMPs are
established for nonlinear surface finite element problems on Riemannian
manifolds, corresponding to the classical pointwise maximum principles on
surfaces in the spirit of Pucci et al. Various real-life examples illustrate
the scope of the results.
