Convergence and superconvergence analyses of Crank–Nicolson mixed Galerkin method for the extended Fisher–Kolmogorov equation
Abstract
In this paper, a Crank–Nicolson mixed Galerkin scheme is proposed, and the convergence and superconvergence error analyses are presented for the extended Fisher–Kolmogorov (EFK) equation in two dimensions. First, the existence and uniqueness of the numerical scheme are studied. Subsequently, some a-priori bounds are obtained in terms of the Lyapunov function. By treating the nonlinear term skilfully and employing the high precision error estimate of the bilinear element on the rectangular mesh, the superclose error estimate is derived rigorously. Furthermore, the global superconvergence result is established using the interpolation post-processing approach. Finally, some numerical results are provided to illustrate the correctness of theoretical findings.
Fields of Study & Subjects
Advanced Numerical Methods in Computational Mathematics
Numerical methods for differential equations
Matrix Theory and Algorithms
Publication details
- Journal / source
- International Journal of Computer Mathematics
- Publisher
- Informa UK Limited
- Volume
- 103
- Issue
- 8
- Pages
- 1668–1689
- Publication date
- 4 March 2026
- Language
- EN