论文标题
准时认证的准抛物线偏微分方程的减少基础方法
A space-time certified reduced basis method for quasilinear parabolic partial differential equations
论文作者
论文摘要
在本文中，我们提出了一种准线性抛物线问题的认证减少基础（RB）方法。该方法基于时空变异公式。我们提供了以时空级别绑定的基于残差的A-tosterii误差，以及该方法认证的相应有效计算估计器。我们使用经验插值方法（EIM）来保证有效的离线在线计算程序。然后将EIM方法的错误严格合并到认证程序中。 Petrov-Galerkin有限元离散化允许从离散问题的曲柄 - 尼科尔森解释中受益，并使用POD-Greedy方法来构建小维度的减少基础空间。它在时间衡量框架中计算降低的基础解决方案，而时空标准中的RB近似误差由估计器控制。因此，所提出的方法将POD-Greedy近似值纳入了时空认证。
In this paper, we propose a certified reduced basis (RB) method for quasilinear parabolic problems. The method is based on a space-time variational formulation. We provide a residual-based a-posteriori error bound on a space-time level and the corresponding efficiently computable estimator for the certification of the method. We use the Empirical Interpolation method (EIM) to guarantee the efficient offline-online computational procedure. The error of the EIM method is then rigorously incorporated into the certification procedure. The Petrov-Galerkin finite element discretization allows to benefit from the Crank-Nicolson interpretation of the discrete problem and to use a POD-Greedy approach to construct the reduced-basis spaces of small dimensions. It computes the reduced basis solution in a time-marching framework while the RB approximation error in a space-time norm is controlled by the estimator. Therefore the proposed method incorporates a POD-Greedy approximation into a space-time certification.
