Numerical discretization for Fisher-Kolmogorov problem with nonlocal diffusion based on mixed Galerkin BDF2 scheme
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Tarih
2024
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Elsevier B.V.
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
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. © 2024 IMACS
Açıklama
Anahtar Kelimeler
BDF2 scheme, Extended Fisher-Kolmogorov equation, Finite element Galerkin method, Nonlocal diffusion
Kaynak
Applied Numerical Mathematics
WoS Q Değeri
Scopus Q Değeri
Q1
Cilt
201
