This paper proposes a novel computational framework for the solution of geometrically parametrised flow problems governed by the Stokes equation. The proposed method uses a high-order hybridisable discontinuous Galerkin formulation and the proper generalised decomposition rationale to construct an off-line solution for a given set of geometric parameters. The generalised solution contains the information for all the geometric parameters in a user-defined range and it can be used to compute sensitivities. The proposed approach circumvents many of the weaknesses of other approaches based on the proper generalised decomposition for computing generalised solutions of geometrically parametrised problems. Four numerical examples show the optimal approximation properties of the proposed method and demonstrate its applicability in two and three dimensions.

中文翻译：

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几何参数化斯托克斯流的可混合不连续伽辽金解

本文提出了一种新的计算框架，用于求解由斯托克斯方程控制的几何参数化流动问题。所提出的方法使用高阶可杂交不连续伽辽金公式和适当的广义分解原理来为给定的几何参数集构建离线解。广义解包含用户定义范围内所有几何参数的信息，可用于计算灵敏度。基于用于计算几何参数化问题的广义解的适当广义分解，所提出的方法规避了其他方法的许多弱点。