A Weak Galerkin Finite Element Method for Solving Nonlinear Convection–Diffusion Problems in One Dimension

Cheichan, Mohammed S.; Kashkool, Hashim A.; Gao, Fuzheng

doi:10.1007/s40819-019-0621-3

Cited by 8 publications

(1 citation statement)

References 19 publications

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“…These finite element functions are chosen to be simple enough to allow for efficient computation and yet provide a good approximation to the true solution. Recently, the Galerkin finite element method was used to solve various problems, and the accuracy and convergence of the method were analyzed, see, for example, [9][10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Numerical approximation of the two-species Shigesada-Kawasaki-Teramoto model

Almusawi

Harfash

2023

Preprint

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In this article, the finite element approximation of the two-species Shigesada-Kawasaki-Teramoto model, with cross-diffusion for one species, is studied. In the beginning, the regularized problem of the model and the entropy proof of the regularized problem were presented. Also, an approxi- mation of the regularized problem using the finite element method was introduced. A number of bounds were found in different spaces for approximate solutions. In addition, depending on the bounds that are obtained, the convergence of the approximate problem to the weak form of the problem was studied, and thus the existence of solutions to the Shigesada-Kawasaki-Teramoto model was proved. Also, a practical algorithm for solving the approximate problem was presented and used to calculate the numerical results of the problem.

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Section: Introductionmentioning

confidence: 99%

Numerical approximation of the two-species Shigesada-Kawasaki-Teramoto model

Almusawi

Harfash

2023

Preprint

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Dynamical analysis of a general delayed HBV infection model with capsids and adaptive immune response in presence of exposed infected hepatocytes

Foko

2024

J. Math. Biol.

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The aim of this paper is to develop and investigate a novel mathematical model of the dynamical behaviors of chronic hepatitis B virus infection. The model includes exposed infected hepatocytes, intracellular HBV DNA-containing capsids, uses a general incidence function for viral infection covering a variety of special cases available in the literature, and describes the interaction of cytotoxic T lymphocytes that kill the infected hepatocytes and the magnitude of B-cells that send antibody immune defense to neutralize free virions. Further, one time delay is incorporated to account for actual capsids production. The other time delays are used to account for maturation of capsids and free viruses. We start with the analysis of the proposed model by establishing the local and global existence, uniqueness, non-negativity and boundedness of solutions. After defined the threshold parameters, we discuss the stability properties of all possible steady state constants by using the crafty Lyapunov functionals, the LaSalle’s invariance principle and linearization methods. The impacts of the three time delays on the HBV infection transmission are discussed through local and global sensitivity analysis of the basic reproduction number and of the classes of infected states. Finally, an application is provided and numerical simulations are performed to illustrate and interpret the theoretical results obtained. It is suggested that, a good strategy to eradicate or to control HBV infection within a host should concentrate on any drugs that may prolong the values of the three delays.

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Weak Galerkin finite element method for solving one-dimensional coupled Burgers’ equations

Hussein

Kashkool

2020

J. Appl. Math. Comput.

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A Weak Galerkin Finite Element Method for Solving Nonlinear Convection–Diffusion Problems in One Dimension

Cited by 8 publications

References 19 publications

Numerical approximation of the two-species Shigesada-Kawasaki-Teramoto model

Numerical approximation of the two-species Shigesada-Kawasaki-Teramoto model

Dynamical analysis of a general delayed HBV infection model with capsids and adaptive immune response in presence of exposed infected hepatocytes

Weak Galerkin finite element method for solving one-dimensional coupled Burgers’ equations

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