Version 1
: Received: 28 August 2024 / Approved: 29 August 2024 / Online: 29 August 2024 (11:32:30 CEST)
How to cite:
Chang, X.; Li, H. The Reduced-Dimension Method for Crank-Nicolson Mixed Finite Element Solution Coefficient Vectors of the Extended Fisher-Kolmogorov Equation. Preprints2024, 2024082117. https://doi.org/10.20944/preprints202408.2117.v1
Chang, X.; Li, H. The Reduced-Dimension Method for Crank-Nicolson Mixed Finite Element Solution Coefficient Vectors of the Extended Fisher-Kolmogorov Equation. Preprints 2024, 2024082117. https://doi.org/10.20944/preprints202408.2117.v1
Chang, X.; Li, H. The Reduced-Dimension Method for Crank-Nicolson Mixed Finite Element Solution Coefficient Vectors of the Extended Fisher-Kolmogorov Equation. Preprints2024, 2024082117. https://doi.org/10.20944/preprints202408.2117.v1
APA Style
Chang, X., & Li, H. (2024). The Reduced-Dimension Method for Crank-Nicolson Mixed Finite Element Solution Coefficient Vectors of the Extended Fisher-Kolmogorov Equation. Preprints. https://doi.org/10.20944/preprints202408.2117.v1
Chicago/Turabian Style
Chang, X. and Hong Li. 2024 "The Reduced-Dimension Method for Crank-Nicolson Mixed Finite Element Solution Coefficient Vectors of the Extended Fisher-Kolmogorov Equation" Preprints. https://doi.org/10.20944/preprints202408.2117.v1
Abstract
A reduced-dimension (RD) method based on the proper orthogonal decomposition (POD) technology and the linearized Crank-Nicolson mixed finite element (CNMFE) scheme for solving the 2D nonlinear Extended Fisher-Kolmogorov (EFK) equation is proposed. The method reduces CPU runtime and error accumulation by reducing the dimension of the unknown CNMFE solution coefficient vectors. For this purpose, The CNMFE scheme of the EFK equation is established and the uniqueness, stability and convergence of the CNMFE solutions are discussed. Subsequently, the matrix-based RDCNMFE scheme is derived by applying the POD method. Furthermore, the uniqueness, stability and error estimates of the linearized RDCNMFE solution are proved. Finally, numerical experiments are carried out to validate the theoretical findings. In addition, we contrast the RDCNMFE method with the CNMFE method, highlighting the advantages of the dimensionality reduction method.
Computer Science and Mathematics, Computational Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
