AI 中文总结
针对扩展Fisher-Kolmogorov方程，基于时间蛙跳和空间混合虚拟元离散化开发线性化保结构算法，证明能量耗散性质并建立无条件最优收敛分析，通过数值例子验证理论及格式性质。
AI 中文摘要
本文基于时间上的蛙跳离散化和空间上的混合虚拟元离散化，开发了一种线性化保结构数值算法。主要贡献在于不仅严格证明了全离散数值格式的能量耗散性质，还通过逆不等式建立了无条件最优收敛分析。证明核心在于对\(\tau\)与\(h\)关系的分类讨论。最后给出两个数值例子验证理论分析正确性及所提格式的能量耗散性质。
英文摘要
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 \(τ\) 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.
