The full discretization of the semi-linear stochastic wave equation is considered. The discontinuous Galerkin finite element method is used in space and analyzed in a semigroup framework, and an explicit stochastic position Verlet scheme is used for the temporal approximation. We study the stability under a CFL condition and prove optimal strong convergence rates of the fully discrete scheme. Numerical experiments illustrate our theoretical results. Further, we analyze and bound the expected energy and numerically show excellent agreement with the energy of the exact solution.

中文翻译：

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半线性随机波动方程的 Verlet 积分器的强收敛

考虑了半线性随机波动方程的完全离散化。空间采用非连续伽辽金有限元法，半群框架分析，时间近似采用显式随机位置Verlet格式。我们研究了 CFL 条件下的稳定性，并证明了完全离散方案的最佳强收敛率。数值实验说明了我们的理论结果。此外，我们分析和限制了预期能量，并在数值上显示出与精确解的能量非常吻合。