Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Error estimate of the Non Intrusive Reduced Basis method with finite
  volume schemes   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).

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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph