Development of numerical analysis by the Galerin-characteristics finite element method

2016 Fiscal Year Final Research Report

• Project/Area Number: 25400212
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Waseda University
• Principal Investigator: Tabata Masahisa 早稲田大学, 理工学術院, 特任教授 (30093272)
• Co-Investigator(Renkei-kenkyūsha): NOTSU Hirofumi 金沢大学, 理工研究域数物科学系, 准教授 (00588783)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: 数値解析 / 特性曲線有限要素法 / 収束性と安定性 / 圧力安定化法 / ナヴィエ・ストークス方程式 / オセーン方程式 / 粘弾性流体 / 風上要素選択法

Outline of Final Research Achievements

We have developed new numerical schemes for flow problems based on the Galerkin characteristics finite element method, which is a combination of the method of characteristics and the finite element method. In these schemes the triangular linear element for 2 dimension problems and the tetrahedron linear element for 3 dimension problems are employed for all unknown functions, which reduces much the computational amount compared to the conventional Galerkin characteristic scheme. We have shown the mathematical validity, the convergence and the error estimate, of the schemes for the Navier-Stokes equations describing the incompressible viscous flows and for an Oseen-type Peterlin model describing a visco-elastic flow. We also recognized the efficiency of the schemes by several numerical computations.

Free Research Field

数値解析