Discrete maximum principle and adequate discretizations of linear parabolic problems
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 …
numerical solutions of linear parabolic problems with Dirichlet-type boundary condition. First …
A review of reliable numerical models for three‐dimensional linear parabolic problems
The preservation of characteristic qualitative properties of different phenomena is a more
and more important requirement in the construction of reliable numerical models. For …
and more important requirement in the construction of reliable numerical models. For …
Continuous and discrete parabolic operators and their qualitative properties
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 …
point of view, it is generally not sufficient to construct convergent numerical methods for the …
[图书][B] On qualitative properties and convergence of time-discretization methods for semigroups
M Kovács - 2004 - search.proquest.com
In this dissertation we use functional calculus methods to investigate convergence and
qualitative properties of time-discretization methods for strongly continuous semigroups …
qualitative properties of time-discretization methods for strongly continuous semigroups …
On weakening conditions for discrete maximum principles for linear finite element schemes
A Hannukainen, S Korotov, T Vejchodský - International Conference on …, 2008 - Springer
In this work we discuss weakening requirements on the set of sufficient conditions due to Ph.
Ciarlet [4, 5] for matrices associated to linear finite element schemes, which is commonly …
Ciarlet [4, 5] for matrices associated to linear finite element schemes, which is commonly …
A bound on powers of linear operators, with relevance to numerical stability
N Borovykh, D Drissi, MN Spijker - Applied Mathematics Letters, 2002 - Elsevier
In this note, we formulate a theorem giving bounds on the powers of linear operators, in a
general Banach space setting. The relevance of the theorem is illustrated by applying it to …
general Banach space setting. The relevance of the theorem is illustrated by applying it to …
[HTML][HTML] Sufficient conditions of the discrete maximum–minimum principle for parabolic problems on rectangular meshes
R Horváth - Computers & Mathematics with Applications, 2008 - Elsevier
New numerical models for simulation of physical and chemical phenomena have to meet
certain qualitative requirements, such as nonnegativity preservation, maximum–minimum …
certain qualitative requirements, such as nonnegativity preservation, maximum–minimum …
On the monotonicity conservation in numerical solutions of the heat equation
R Horváth - Applied numerical mathematics, 2002 - Elsevier
It is important to choose such numerical methods in practice that mirror the characteristic
properties of the described process beyond the stability and convergence. The investigated …
properties of the described process beyond the stability and convergence. The investigated …
A new insight on positivity and contractivity of the Crank-Nicolson scheme for the heat equation
I Higueras, T Roldán - arXiv preprint arXiv:2301.01066, 2023 - arxiv.org
In this paper we study numerical positivity and contractivity in the infinite norm of Crank-
Nicolson method when it is applied to the diffusion equation with homogeneous Dirichlet …
Nicolson method when it is applied to the diffusion equation with homogeneous Dirichlet …
[HTML][HTML] Qualitative properties of nonlinear parabolic operators
It is a natural expectation that the mathematical models of real-life phenomena have to
possess some characteristic qualitative properties of the original process. For parabolic …
possess some characteristic qualitative properties of the original process. For parabolic …