Discrete Maximum Principle and Adequate Discretizations of Linear Parabolic Problems
SIAM Journal on Scientific Computing
Discrete maximum principle for linear parabolic problems solved on hybrid meshes
Applied Numerical Mathematics
Discrete maximum principle for finite element parabolic models in higher dimensions
Mathematics and Computers in Simulation
Discrete and continuous maximum principles for parabolic and elliptic operators
Journal of Computational and Applied Mathematics
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When we construct continuous and/or discrete mathematical models in order to describe a real-life problem, these models should possess various qualitative properties, which typically arise from some basic principles of the modelled phenomenon In this paper we investigate this question for the numerical solution of initial-boundary value problems for parabolic equations with nonzero convection and reaction terms with function coefficients in higher dimensions The Dirichlet boundary condition will be imposed, and we will solve the problem by using linear finite elements and the θ-method The principally important qualitative properties for this problem are the non-negativity preservation and different maximum principles We give the conditions for the geometry of the mesh and for the choice of the discretization parameters, i.e., for θ and the time-step sizes, under which these discrete qualitative properties hold Finally, we give numerical examples to investigate how sharp our conditions are.