Error estimate of the non-intrusive reduced basis method with finite volume schemes
نویسندگان
چکیده
The context of this paper is the simulation parameter-dependent partial differential equations (PDEs). When aim to solve such PDEs for a large number parameter values, Reduced Basis Methods (RBM) are often used reduce computational costs classical high fidelity code based on Finite Element Method (FEM), Volume (FVM) or Spectral methods. efficient implementation most these RBM requires modify code, which cannot be done, example in an industrial if only accessible as "black-box" solver. Non-Intrusive (NIRB) method has been introduced finite elements good alternative problems. other contexts than FEM one, like with volume schemes, more environment. In case, some adaptations need done degrees freedom FV methods have different meanings. At time, error estimates studied solvers. paper, we present generalisation NIRB schemes and show that established solvers also hold FVM setting. We first prove our results hybrid-Mimetic Difference (hMFD), part Hybrid Mixed Mimetic (HMM) family. Then, explain how apply generally schemes. Some them specified, Two Point Flux Approximation (TPFA).
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Error estimate for finite volume scheme
The Finite Volume method is well adapted to the computation of the solution of pdes which are conservation (or balance) laws, for the reason that it respects the property of conservation of the pde under study. The mathematical analysis of the application of the Finite Volume method to hyperbolic first-order conservation laws can be dated from the mid sixties (see [TS62] for example). Concernin...
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ژورنال
عنوان ژورنال: Mathematical Modelling and Numerical Analysis
سال: 2021
ISSN: ['0764-583X', '1290-3841']
DOI: https://doi.org/10.1051/m2an/2021044