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Journal of Scientific Computing

Erschienen in:

09.06.2017

Multigrid Methods for a Mixed Finite Element Method of the Darcy–Forchheimer Model

verfasst von: Jian Huang, Long Chen, Hongxing Rui

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2018

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Abstract

An efficient nonlinear multigrid method for a mixed finite element method of the Darcy–Forchheimer model is constructed in this paper. A Peaceman–Rachford type iteration is used as a smoother to decouple the nonlinearity from the divergence constraint. The nonlinear equation can be solved element-wise with a closed formulae. The linear saddle point system for the constraint is reduced into a symmetric positive definite system of Poisson type. Furthermore an empirical choice of the parameter used in the splitting is proposed and the resulting multigrid method is robust to the so-called Forchheimer number which controls the strength of the nonlinearity. By comparing the number of iterations and CPU time of different solvers in several numerical experiments, our multigrid method is shown to convergent with a rate independent of the mesh size and the Forchheimer number and with a nearly linear computational cost.

Vorheriger Artikel A Sequential Discontinuous Galerkin Method for the Coupling of Flow and Geomechanics

Nächster Artikel Tensor Methods for Solving Symmetric -tensor Systems

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Titel: Multigrid Methods for a Mixed Finite Element Method of the Darcy–Forchheimer Model
verfasst von: Jian Huang
Long Chen
Hongxing Rui
Publikationsdatum: 09.06.2017
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2018
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-017-0466-z

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