A potential exploring of a multi-dimensional coupled Burgers–Fisher–Huxley equation using finite volume and element methods (FVM/FEM)
Abstract
The purpose of this work is to examine an intensive investigation of the framework based on Finite Element (FE) and Finite Volume (FV) methods to solve the generalized Burgers-Fisher-Huxley (BFH) equation. These methods are explored here to approximate these solutions in higher dimensional space, highlighting some of their properties on the existence and uniqueness of bounded and positive solutions. Convergent numerical schemes are presented. Particularly, the second-order FV scheme is achieved by implementing a predictor-corrector method. In which slightly different forms of the limiter solvers are applied to resolve the leftright degeneracy on the interface by solving the Riemann problem. The purpose of using a limiter is to reduce the slope near the extrema, which is shown on FV grid with the original data. An FE scheme capable of preserving this property, which is directly related to the continuous Galerkin (CG) and indirectly to discontinuous Galerkin (DG), is proposed. Highly accurate solutions are obtained by the framework that shows its flexibility in solving different problems. The convergence behavior is observed between all the methods by controlling viscosity to demonstrate a striking agreement between the numerical and analytical solutions.
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BibTeX
@article{chakkour2026potential,
title = {{A potential exploring of a multi-dimensional coupled Burgers–Fisher–Huxley equation using finite volume and element methods (FVM/FEM)}},
author = {Tarik Chakkour},
journal = {Results in Applied Mathematics},
year = {2026},
month = aug,
doi = {10.1016/j.rinam.2026.100753},
url = {https://hal.science/hal-05776918v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - JOUR
TI - A potential exploring of a multi-dimensional coupled Burgers–Fisher–Huxley equation using finite volume and element methods (FVM/FEM)
AU - Tarik Chakkour
PY - 2026
DA - 2026/08/21
JO - Results in Applied Mathematics
DO - 10.1016/j.rinam.2026.100753
UR - https://hal.science/hal-05776918v1
AB - The purpose of this work is to examine an intensive investigation of the framework based on Finite Element (FE) and Finite Volume (FV) methods to solve the generalized Burgers-Fisher-Huxley (BFH) equation. These methods are explored here to approximate these solutions in higher dimensional space, highlighting some of their properties on the existence and uniqueness of bounded and positive solutions. Convergent numerical schemes are presented. Particularly, the second-order FV scheme is achieved by implementing a predictor-corrector method. In which slightly different forms of the limiter solvers are applied to resolve the leftright degeneracy on the interface by solving the Riemann problem. The purpose of using a limiter is to reduce the slope near the extrema, which is shown on FV grid with the original data. An FE scheme capable of preserving this property, which is directly related to the continuous Galerkin (CG) and indirectly to discontinuous Galerkin (DG), is proposed. Highly accurate solutions are obtained by the framework that shows its flexibility in solving different problems. The convergence behavior is observed between all the methods by controlling viscosity to demonstrate a striking agreement between the numerical and analytical solutions.
SN - 2590-0374
ER -