Discrete conservation and discrete maximum principle for elliptic PDEs. (English) Zbl 0939.65123

Bertolazzi, Enrico

Math. Models Methods Appl. Sci. 8, No. 4, 685-711 (1998).

Summary: A class of finite volume numerical schemes for the solution of selfadjoint elliptic equations is described. The main feature of the schemes is that numerical solutions share both discrete conservation and discrete strong maximum principles without restriction on the differential operator or on the volume elements.

MSC:

65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25	Boundary value problems for second-order elliptic equations
65N06	Finite difference methods for boundary value problems involving PDEs

Keywords:

conservative finite volume method; second-order elliptic equation; Dirichlet problem; maximum principles