论文标题
适用于一类慢速抛物线半线性SPDES的渐近保存方案的均匀弱误差估计值
Uniform weak error estimates for an asymptotic preserving scheme applied to a class of slow-fast parabolic semilinear SPDEs
论文作者
论文摘要
我们研究了一种具有两个时间尺度的抛物线抛物线半线性SPDES系统的渐近保存方案。由于平均原理，当时间尺度分离$ε$消失时，缓慢的组件会收敛到限制进化方程的解决方案，当时间键尺寸$ΔT$通过限制方案消失时，该方程将被捕获。这项工作的目的是证明相对于$ε$均匀的弱误差估计，就$ΔT$而言：该方案满足了均匀的精度属性。这是对无限维度框架中最新文章的无聊概括。快速组件使用最近在一项工作中引入的SPDE的修改Euler方案离散化。证明较弱的误差估计需要微妙分析无限尺寸kolmogorov方程的溶液的规律性。
We study an asymptotic preserving scheme for the temporal discretization of a system of parabolic semilinear SPDEs with two time scales. Owing to the averaging principle, when the time scale separation $ε$ vanishes, the slow component converges to the solution of a limiting evolution equation, which is captured when the time-step size $Δt$ vanishes by a limiting scheme. The objective of this work is to prove weak error estimates which are uniform with respect to $ε$, in terms of $Δt$: the scheme satisfies a uniform accuracy property. This is a non trivial generalization of a recent article in an infinite dimensional framework. The fast component is discretized using the modified Euler scheme for SPDEs introduced in a recent work. Proving the weak error estimates requires delicate analysis of the regularity properties of solutions of infinite dimensional Kolmogorov equations.
