One of the most important problems in numerical simulations is the preservation of
qualitative properties of solutions of the mathematical models by computed approximations …

In this paper, we analyze the connections between the different qualitative properties of
numerical solutions of linear parabolic problems with Dirichlet-type boundary condition. First …

The cutoff method, which cuts off the values of a function less than a given number, is
studied for the numerical computation of nonnegative solutions of parabolic partial …

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 …

The preservation of characteristic qualitative properties of different phenomena is a more
and more important requirement in the construction of reliable numerical models. For …

The basic requirement of numerical methods is convergence. However, from the practical
point of view, it is generally not sufficient to construct convergent numerical methods for the …

Preservation of basic qualitative properties (for example, the maximum principle) ofthe
solution of partial differential equations by its finite-element approximations is an important …

In this article, we derive and discuss sufficient conditions for providing validity of the discrete
maximum principle for nonstationary diffusion‐reaction problems with mixed boundary …

Modifications to the standard finite element mass matrix are considered with the aim of
preserving the positivity of the discrete solution. The approach is used in connection with …

In this paper we analyze the discrete maximum principle (DMP) for a non-stationary diffusion–
reaction problem solved by means of prismatic finite elements and θ-method. We derive …