Discrete maximum principles for nonlinear elliptic finite element problems on Riemannian manifolds with boundary
Provides theoretical guarantees for numerical solutions of nonlinear elliptic equations on surfaces, benefiting computational scientists working on geometric PDEs.
The paper establishes discrete maximum principles (DMPs) for nonlinear surface finite element problems on Riemannian manifolds, extending classical pointwise maximum principles to discrete settings. The results are illustrated with real-life examples.
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.