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We perform an error analysis of a fully discretised Streamline Upwind Petrov Galerkin Dynamical Low Rank (SUPG-DLR) method for random time-dependent advection-dominated problems. The time integration scheme has a splitting-like nature, allowing for potentially efficient computations of the factors characterising the discretised random field. The method allows to efficiently compute a low-rank approximation of the true solution, while naturally “inbuilding” the SUPG stabilisation. Standard error rates in the \(\Vert \cdot \Vert _{L^2}\) and \(\Vert \cdot \Vert _{\textrm{SUPG}}\) -norms are recovered. Numerical experiments validate the predicted rates.

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Error Estimates for SUPG-Stabilised Dynamical Low Rank Approximations

  • 会议论文

  • 发表日期：

    2025年

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  • Fabio Nobile,
  • Thomas Trigo Trindade

摘要

We perform an error analysis of a fully discretised Streamline Upwind Petrov Galerkin Dynamical Low Rank (SUPG-DLR) method for random time-dependent advection-dominated problems. The time integration scheme has a splitting-like nature, allowing for potentially efficient computations of the factors characterising the discretised random field. The method allows to efficiently compute a low-rank approximation of the true solution, while naturally “inbuilding” the SUPG stabilisation. Standard error rates in the \(\Vert \cdot \Vert _{L^2}\) and \(\Vert \cdot \Vert _{\textrm{SUPG}}\) -norms are recovered. Numerical experiments validate the predicted rates.