2017 Fiscal Year Final Research Report
Development of Lagrange-Galerkin methods for non-Newtonian fluid flows
| Project/Area Number |
26800091
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Kanazawa University (2016-2017)
Waseda University (2014-2015) |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Keywords | 粘弾性流体 / 有限要素法 / 特性曲線 / 誤差評価 |
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| Outline of Final Research Achievements |
The purpose of this research is development, analysis and computation of Lagrange-Galerkin schemes for non-Newtonian fluid flow models, where the meaning of Lagrange-Galerkin scheme is a finite element scheme based on the method of characteristics. For that purpose, we proposed nonlinear and linear Lagrange-Galerkin schemes for a non-Newtonian fluid flow model called the Peterlin viscoelastic model after the establishment of the optimal error estimates of the stabilized Lagrange-Galerkin scheme for the Navier-Stokes equations. We finally obtained the optimal error estimates of the two Lagrange-Galerkin schemes for a simplified (Oseen-type) Peterlin viscoelastic model. The theoretical results as well as numerical results were summarized in the two papers published in the journal ESAIM: M2AN.
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| Free Research Field |
数値解析
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