论文标题
半线性随机波方程的Verlet积分器的强收敛
Strong convergence of a Verlet integrator for the semi-linear stochastic wave equation
论文作者
论文摘要
考虑了半线性随机波方程的全部离散化。不连续的Galerkin有限元法用于空间并在半群框架中进行分析，并且使用明确的随机位置Verlet方案用于时间近似。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速率。数值实验说明了我们的理论结果。此外，我们分析并结合预期能量，并在数值上与精确溶液的能量显示出极好的一致性。
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.
