[图书][B] Algebraic flux correction I: Scalar conservation laws
D Kuzmin - 2012 - Springer
This chapter is concerned with the design of high-resolution finite element schemes
satisfying the discrete maximum principle. The presented algebraic flux correction paradigm …
satisfying the discrete maximum principle. The presented algebraic flux correction paradigm …
Explicit and implicit FEM-FCT algorithms with flux linearization
D Kuzmin - Journal of Computational Physics, 2009 - Elsevier
A new approach to the design of flux-corrected transport (FCT) algorithms for continuous
(linear/multilinear) finite element approximations of convection-dominated transport …
(linear/multilinear) finite element approximations of convection-dominated transport …
Discrete maximum principles for finite element solutions of nonlinear elliptic problems with mixed boundary conditions
J Karátson, S Korotov - Numerische Mathematik, 2005 - Springer
One of the most important problems in numerical simulations is the preservation of
qualitative properties of solutions of the mathematical models by computed approximations …
qualitative properties of solutions of the mathematical models by computed approximations …
A constrained finite element method satisfying the discrete maximum principle for anisotropic diffusion problems
D Kuzmin, MJ Shashkov, D Svyatskiy - Journal of Computational Physics, 2009 - Elsevier
Nonlinear constrained finite element approximations to anisotropic diffusion problems are
considered. Starting with a standard (linear or bilinear) Galerkin discretization, the entries of …
considered. Starting with a standard (linear or bilinear) Galerkin discretization, the entries of …
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 …
The cutoff method for the numerical computation of nonnegative solutions of parabolic PDEs with application to anisotropic diffusion and lubrication-type equations
C Lu, W Huang, ES Van Vleck - Journal of Computational Physics, 2013 - Elsevier
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 …
studied for the numerical computation of nonnegative solutions of parabolic partial …
High order maximum-principle-preserving discontinuous Galerkin method for convection-diffusion equations
In this paper, we propose to apply the parametrized maximum-principle-preserving (MPP)
flux limiter in [T. Xiong, J.-M. Qiu, and Z. Xu, J. Comput. Phys., 252 (2013), pp. 310--331] to …
flux limiter in [T. Xiong, J.-M. Qiu, and Z. Xu, J. Comput. Phys., 252 (2013), pp. 310--331] to …
Discrete maximum principles for nonlinear parabolic PDE systems
Discrete maximum principles (DMPs) are established for finite element approximations of
systems of nonlinear parabolic partial differential equations with mixed boundary and …
systems of nonlinear parabolic partial differential equations with mixed boundary and …
Linearity-preserving monotone local projection stabilization schemes for continuous finite elements
This paper presents some new tools for enforcing discrete maximum principles and/or
positivity preservation in continuous piecewise-linear finite element approximations to …
positivity preservation in continuous piecewise-linear finite element approximations to …
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 …