Journal of Computational and Applied Mathematics - Special issue on computational and mathematical methods in science and engineering (CMMSE-2004)
A weak discrete maximum principle for hp-FEM
Journal of Computational and Applied Mathematics
On discrete maximum principles for nonlinear elliptic problems
Mathematics and Computers in Simulation
Discrete conservation of nonnegativity for elliptic problems solved by the hp-FEM
Mathematics and Computers in Simulation
On Weakening Conditions for Discrete Maximum Principles for Linear Finite Element Schemes
Numerical Analysis and Its Applications
Numerical Analysis and Its Applications
Discrete maximum principle for FE solutions of the diffusion-reaction problem on prismatic meshes
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Non-negative mixed finite element formulations for a tensorial diffusion equation
Journal of Computational Physics
Higher-order discrete maximum principle for 1D diffusion--reaction problems
Applied Numerical Mathematics
Journal of Computational Physics
Matrix and discrete maximum principles
LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
A discrete maximum principle for nonlinear elliptic systems with interface conditions
LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
SIAM Journal on Numerical Analysis
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One of the most important problems in numerical simulations is the preservation of qualitative properties of solutions of the mathematical models by computed approximations. For problems of elliptic type, one of the basic properties is the (continuous) maximum principle. In our work, we present several variants of the maximum principles and their discrete counterparts for (scalar) second-order nonlinear elliptic problems with mixed boundary conditions. The problems considered are numerically solved by the continuous piecewise linear finite element approximations built on simplicial meshes. Sufficient conditions providing the validity of the corresponding discrete maximum principles are presented. Geometrically, they mean that the employed meshes have to be of acute or nonobtuse type, depending of the type of the problem. Finally some examples of real-life problems, where the preservation of maximum principles plays an important role, are presented.