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arXiv · 2607.09044

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

Zhen Guan·Xianxian Cao·Houchao Zhang·Junjun Wang
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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.

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Zhen Guan, Xianxian Cao, Houchao Zhang, Junjun Wang. 2026-07-10. A Linearized and structure-preserving mixed virtual element method for the extended Fisher-Kolmogorov equation. https://arxiv.org/abs/2607.09044

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