Abstract In this manuscript, we consider an efficient dissipation-preserving finite element method for a class of two-dimensional nonlinear fractional wave equations on irregular convex domains. We show that the fully discrete method preserves the discrete energy structures under the same boundary conditions as the continuous model. Furthermore, the optimal order error estimates of the fully discrete scheme are proved in detail. Finally, the numerical simulations, which are based on spatial unstructured meshes, are presented to confirm the correctness of the theoretical results.

中文翻译：

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不规则凸域上非线性分数阶波动方程的一种耗散保持有限元方法

摘要 在这篇手稿中，我们考虑了一类在不规则凸域上的二维非线性分数阶波动方程的有效耗散保持有限元方法。我们表明，完全离散的方法在与连续模型相同的边界条件下保留了离散的能量结构。此外，详细证明了完全离散方案的最优阶误差估计。最后，给出了基于空间非结构化网格的数值模拟，以证实理论结果的正确性。