The context of this paper is the simulation of parameter-dependent partial differential equations (PDEs). When the aim is to solve such PDEs for a large number of parameter values, Reduced Basis Methods (RBM) are often used to reduce computational costs of a classical high fidelity code based on Finite Element Method (FEM), Finite Volume (FVM) or Spectral methods. The efficient implementation of most of these RBM requires to modify this high fidelity code, which cannot be done, for example in an industrial context if the high fidelity code is only accessible as a ''black-box'' solver. The Non Intrusive Reduced Basis method (NIRB) has been introduced in the context of finite elements as a good alternative to reduce the implementation costs of these parameter-dependent problems. The method is efficient in other contexts than the FEM one, like with finite volume schemes, which are more often used in an industrial environment. In this case, some adaptations need to be done as the degrees of freedom in FV methods have different meenings. At this time, error estimates have only been studied with FEM solvers. In this paper, we present a generalisation of the NIRB method to Finite Volume schemes and we show that estimates established for FEM solvers also hold in the FVM setting. We first prove our results for the hybrid-Mimetic Finite Difference method (hMFD), which is part the Hybrid Mixed Mimetic methods (HMM) family. Then, we explain how these results apply more generally to other FV schemes. Some of them are specified, such as the Two Point Flux Approximation (TPFA).

翻译：本文的上下文是基于参数的局部偏差方程式( PDEs) 的模拟。 当旨在为大量参数值解决这种 PDEs 时, 通常会使用 降低基础法( RBM ) 来降低基于精度元素法( FEM )、 精度量法( FVM ) 或光谱法的古典高忠诚代码的计算成本。 大多数这种成果管理制的有效实施都需要修改这种高忠诚度代码, 而在工业环境中, 无法做到这一点。 例如, 如果高忠诚度代码仅作为“ back-box” 解答器使用, 则在工业环境中, 高忠诚度代码无法做到。 当高忠诚度代码仅作为“ black-box” 解析器来解析时, 低侵犯性减少基准法( RBM ) 通常在限定要素值范围内, 将FEMM 方法的误算值值值值值值值值值用于 FEMM 。