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On continuous and discrete maximum/minimum principles for reaction-diffusion problems with the Neumann boundary condition. (English) Zbl 1363.35061
Brandts, J. (ed.) et al., Proceedings of the international conference ‘Applications of mathematics’, Prague, Czech Republic, November 18–21, 2015. In honor of the birthday anniversaries of Ivo Babuška (90), Milan Práger (85), and Emil Vitásek (85). Prague: Czech Academy of Sciences, Institute of Mathematics (ISBN 978-80-85823-65-3). 34-44 (2015).
Continuous and discrete maximum/minimum principles for a class of boundary-value problems of elliptic type with Neumann boundary conditions are treated. The main results in this work are related to discrete versions of the maximum/minimum principles. The authors obtain practical conditions on schemes used in the finite element method (FEM) and finite difference method (FDM). The paper opens perspectives for extensions of the results obtained to \(hp\)-versions of FEM and to more general elliptic problems.
For the entire collection see [Zbl 1329.00187].

MSC:
35B50 Maximum principles in context of PDEs
65N06 Finite difference methods for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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