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Numerical discretization for Fisher-Kolmogorov problem with nonlocal diffusion based on mixed Galerkin BDF2 scheme.
- Source :
-
Applied Numerical Mathematics . Jul2024, Vol. 201, p145-158. 14p. - Publication Year :
- 2024
-
Abstract
- Nonlocal problems involving fourth-order terms pose several difficulties such as numerical discretization and its related convergences analysis. In this paper, the well-posedness of the extended Fisher-Kolmogorov equation with nonlocal diffusion is first analyzed using the Faedo-Galerkin technique and the classical compactness arguments. Moreover, we adopt a BDF2 scheme for time discretization and a mixed Galerkin scheme for spatial discretization. Then, we derive the optimal order convergence rates of the fully discrete system. Finally, some numerical simulations and convergence results are provided to confirm the theoretical results and the accuracy of the proposed scheme. [ABSTRACT FROM AUTHOR]
- Subjects :
- *HEAT equation
*DISCRETE systems
*FINITE element method
*COMPUTER simulation
Subjects
Details
- Language :
- English
- ISSN :
- 01689274
- Volume :
- 201
- Database :
- Academic Search Index
- Journal :
- Applied Numerical Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 176991858
- Full Text :
- https://doi.org/10.1016/j.apnum.2024.02.018