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- W4319323265 abstract "This work introduces a general framework for establishing the long time accuracy for approximations of Markovian dynamical systems on separable Banach spaces. Our results illuminate the role that a certain uniformity in Wasserstein contraction rates for the approximating dynamics bears on long time accuracy estimates. In particular, our approach yields weak consistency bounds on $mathbb{R}^+$ while providing a means to sidestepping a commonly occurring situation where certain higher order moment bounds are unavailable for the approximating dynamics. Additionally, to facilitate the analytical core of our approach, we develop a refinement of certain `weak Harris theorems'. This extension expands the scope of applicability of such Wasserstein contraction estimates to a variety of interesting SPDE examples involving weaker dissipation or stronger nonlinearity than would be covered by the existing literature. As a guiding and paradigmatic example, we apply our formalism to the stochastic 2D Navier-Stokes equations and to a semi-implicit in time and spectral Galerkin in space numerical approximation of this system. In the case of a numerical approximation, we establish quantitative estimates on the approximation of invariant measures as well as prove weak consistency on $mathbb{R}^+$. To develop these numerical analysis results, we provide a refinement of $L^2_x$ accuracy bounds in comparison to the existing literature which are results of independent interest." @default.
- W4319323265 created "2023-02-08" @default.
- W4319323265 creator A5058571963 @default.
- W4319323265 creator A5079585562 @default.
- W4319323265 date "2023-02-02" @default.
- W4319323265 modified "2023-09-27" @default.
- W4319323265 title "Long-term accuracy of numerical approximations of SPDEs with the stochastic Navier-Stokes equations as a paradigm" @default.
- W4319323265 doi "https://doi.org/10.48550/arxiv.2302.01461" @default.
- W4319323265 hasPublicationYear "2023" @default.
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