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Finite Element Methods Respecting the Discrete Maximum Principle for Convection-Diffusion Equations

SIAM Review
Convection-diffusion-reaction equations model the conservation of scalar quantities. From the analytic point of view, solution of these equations satisfy under certain conditions maximum principles, which represent physical bounds of the solution.
Gabriel R Barrenechea, Volker John, Petr Knobloch   +2 more
exaly   +2 more sources

Weak solutions for diffusion-convection equations

Applied Mathematics Letters, 2000
Weak solutions to diffusion-convection equations with less regular convective field and boundary data are shown to exist as limits of solutions to problems with mixed boundary ...
Ito, K., Ito, Kazufumi, Fang, Weifu, Fang, W.   +3 more
exaly   +2 more sources

Method of approximations for the convection-dominated anomalous diffusion equation in a rectangular plate using high-resolution compact discretization

MethodsX, 2022
The present method describes the high-resolution compact discretization method for the numerical solution of the nonlinear fractal convection-diffusion model on a rectangular plate by employing the Hausdorff distance metric.
Navnit Jha, Shikha Verma
doaj   +1 more source

Novel Numerical Method Based on the Analog Equation Method for a Class of Anisotropic Convection-Diffusion Problems

Frontiers in Physics, 2022
In this work, a CMFS method based on the analogy equation method, the radial basis function and the method of fundamental solutions for linear and nonlinear convection-diffusion equations in anisotropic materials is presented.
L Zhang, L Zhang, FZ Wang, FZ Wang, J Zhang, J Zhang, YY Wang, S Nadeem, TA Nofal   +8 more
doaj   +1 more source

New traveling wave solutions of a nonlinear diffusion–convection equation by using standard tanh method

Tikrit Journal of Pure Science, 2023
Exact solutions of traveling wave are acquired by employ a relatively new technique which is called standard tanh method for a nonlinear diffusion–convection equation.
Seham I. Aziz, Wafaa M. Taha, Raad A. Hameed, Ibrahem M. Taha   +3 more
doaj   +1 more source

Exact traveling wave solutions of fast reaction–diffusion–convectionequations based on the Lambert function W

Partial Differential Equations in Applied Mathematics, 2020
A particular function defined in terms of the Lambert function W is shown to serve as the basis for exact traveling wave solutions to several reaction–diffusion–convection​ (RDC) equations involving rational, non-linear diffusion terms. These represent a
Brian Wesley Williams
doaj   +1 more source

Error analysis of a SUPG-stabilized POD-ROM method for convection-diffusion-reaction equations [PDF]

, 2021
A reduced order model (ROM) method based on proper orthogonal decomposition (POD) is analyzed for convection-diffusion-reaction equations. The streamline-upwind Petrov--Galerkin (SUPG) stabilization is used in the practically interesting case of dominant
Novo, Julia, Baptiste Moreau, Novo Martín, Julia, Volker John, Moreau, Baptiste, Julia Novo, John, Volker   +6 more
core   +1 more source

G-jitter induced magnetohydrodynamics flow of nanofluid with constant convective thermal and solutal boundary conditions. [PDF]

PLoS ONE, 2015
Taking into account the effect of constant convective thermal and mass boundary conditions, we present numerical solution of the 2-D laminar g-jitter mixed convective boundary layer flow of water-based nanofluids.
Mohammed J Uddin, Waqar A Khan, Ahmad Izani Md Ismail   +2 more
doaj   +1 more source

Compact and stable discontinuous Galerkin methods for convection-diffusion problems [PDF]

, 2012
We present a new scheme, the compact discontinuous Galerkin 2 (CDG2) method, for solving nonlinear convection-diffusion problems together with a detailed comparison to other well-accepted DG methods.
Dedner, A., Dedner, Andreas, Klöfkorn, R., Brdar, S.   +3 more
core   +1 more source

Using Deep Neural Networks for Detecting Spurious Oscillations in Discontinuous Galerkin Solutions of Convection-Dominated Convection–Diffusion Equations

, 2023
Standard discontinuous Galerkin finite element solutions to convection-dominated convection–diffusion equations usually possess sharp layers but also exhibit large spurious oscillations.
Frerichs-Mihov, Derk, Henning, Linus, John, Volker   +2 more
core   +1 more source