×

Discrete maximum principles for FEM solutions of some nonlinear elliptic interface problems. (English) Zbl 1163.65076

Discrete maximum principles are proved for finite element discretizations of some semilinear elliptic differential equations. Nonlinearities are admitted in jumps of normal derivatives and in reaction terms. In esssence, it is assumed that the discretization of the (second) derivatives leads to \(M\)-matrices. Therefore, finite elements with piecewise linear basis functions are considered and conditions on geometric properties of the mesh are discussed.

MSC:

65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J65 Nonlinear boundary value problems for linear elliptic equations
35B50 Maximum principles in context of PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
PDFBibTeX XMLCite
Full Text: Link