Abstract
A fourth-order diffusion model is presented with a nonlinear reaction term to simulate some special chemical and biological phenomenon. To obtain the solutions to those problems, the nonlinear Galerkin finite element method under the framework of the Hermite polynomial function for the spatial domain is utilized. The Euler backward difference method is used to solve the equation in the temporal domain. Subject to the Dirichlet and Navier boundary conditions, the numerical experiments for Bi-flux Fisher–Kolmogorov model present excellent convergence, accuracy and acceleration behavior. Also, the numerical solutions to the Bi-flux Gray–Scott model, subject to no flux boundary conditions, show excellent convergence, accuracy and symmetry.
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Acknowledgements
Jiang Zhu’s work was partially supported by the National Council for Scientific and Technological Development of Brazil (CNPq). Xijun Yu’s work was supported partially by the National Natural Science Foundation of China (Grant No. 11571002, 11772067, 11702028) and CAEP Foundation of China (Grant No. CX2019032). Luiz Bevilacqua’s work was supported partially by CNPq/TWAS Grant, the COPPE/CAPES Grant 001, and the USP/IEA visiting research program. Maosheng Jiang’s work was supported partially by CNPq/TWAS Grant.
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Communicated by Abimael Loula.
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Jiang, M., Bevilacqua, L., Zhu, J. et al. Nonlinear Galerkin finite element methods for fourth-order Bi-flux diffusion model with nonlinear reaction term. Comp. Appl. Math. 39, 143 (2020). https://doi.org/10.1007/s40314-020-01168-w
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DOI: https://doi.org/10.1007/s40314-020-01168-w