A Linearized and structure-preserving mixed virtual element method for the extended Fisher-Kolmogorov equation

Zhen Guan; Xianxian Cao; Houchao Zhang; Junjun Wang

A Linearized and structure-preserving mixed virtual element method for the extended Fisher-Kolmogorov equation

Numerical Analysis 2026-07-10 v1

Authors: Zhen Guan , Xianxian Cao , Houchao Zhang , Junjun Wang

Abstract

In thsi paper, based on the leap-frog discretization in time and the mixed virtual element discretization in space, we developed a linearized and structure-preserving numerical algorithm. The main contributions of this work lie in that we not only provide a rigorous proof of the energy dissipation property of the fully discrete numerical scheme, but also establish the unconditionally optimal convergence analysis by means of a inverse inequality. The core of the proof lies in the classified discussion of the relationship between $\tau$ and $h$ . Finally, two numerical examples are provided to validate the correctness of the theoretical analysis as well as the energy dissipation property of the proposed scheme.

Keywords

extended Fisher-Kolmogorov equation mixed virtual element method structure-preserving energy dissipation convergence analysis linearized scheme

Cite

@article{arxiv.2607.09044,
  title  = {A Linearized and structure-preserving mixed virtual element method for the extended Fisher-Kolmogorov equation},
  author = {Zhen Guan and Xianxian Cao and Houchao Zhang and Junjun Wang},
  journal= {arXiv preprint arXiv:2607.09044},
  year   = {2026}
}