Error estimate of the Non Intrusive Reduced Basis method with finite volume schemes

by   Elise Grosjean, et al.

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).


page 16

page 17


A Least-Squares Finite Element Reduced Basis Method

We present a reduced basis (RB) method for parametrized linear elliptic ...

Error estimate of the Non-Intrusive Reduced Basis (NIRB) two-grid method with parabolic equations

Reduced Basis Methods (RBMs) are frequently proposed to approximate para...

Error Approximation and Bias Correction in Dynamic Problems using a Recurrent Neural Network/Finite Element Hybrid Model

This work proposes a hybrid modeling framework based on recurrent neural...

A non-intrusive bi-fidelity reduced basis method for time-independent problems

Scientific and engineering problems often involve parametric partial dif...

Poly-Spline Finite Element Method

We introduce an integrated meshing and finite element method pipeline en...

A novel reduced order model for vortex induced vibrations of long flexible cylinders

In this manuscript the development of a reduced order model for the anal...

Enhancing CFD predictions in shape design problems by model and parameter space reduction

In this work we present an advanced computational pipeline for the appro...

Please sign up or login with your details

Forgot password? Click here to reset