Discrete maximum principle for linear parabolic problems solved on hybrid meshes

The preservation of qualitative characteristics, such as the maximum principle, of the solutions of mathematical models in computer simulations is one of the key requirements. In our work, we present the discrete analogue of the maximum principle for linear parabolic problems and derive the necessary and sufficient conditions for its validity in terms of matrices arising in the corresponding computational schemes. The particular case of Galerkin-type schemes and hybrid unstructured meshes, consisting of triangular and rectangular elements, are analysed.