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A New L^(2)Projection Method for the oseen equations

Advances in Applied Mathematics and Mechanics 2017年第6期9卷 1420-1437页

作者： Yanhong Bai Minfu Feng College of Sciences and Institute of Nonlinear DynamicsSouthwest Petroleum UniversityChengduSichuan 610500China School of Mathematics Sichuan UniversityChengduSichuan 610064China

In this paper,a new type of stabilized finite element method is discussed for oseen equations based on the local L^(2)projection stabilized technique for the velocity *** and pressure are approximated by two kinds of mixed finite element spaces,P^(2)_( l)-P_(1),(l=1,2).A main advantage of the proposed method lies in that,all the computations are performed at the same element level,without the need of nested meshes or the projection of the gradient of velocity onto a coarse *** and convergence are proved for two kinds of stabilized *** experiments confirm the theoretical results.

关键词： oseen equations L^(2)projection method pressure projection method

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A Parallel Finite Element Algorithm for the Unsteady oseen equations

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Advances in Applied Mathematics and Mechanics 2021年第6期13卷 1501-1519页

作者： Qi Ding Yueqiang Shang School of Mathematics and Statistics Southwest UniversityChongqing 400715China Tongnan Middle School Chongqing 402660China

Based on fully overlapping domain decomposition,a parallel finite element algorithm for the unsteady oseen equations is proposed and *** this algorithm,each processor independently computes a finite element approximate solution in its own subdomain by using a locally refined multiscale mesh at each time step,where conforming finite element pairs are used for the spatial discretizations and backward Euler scheme is used for the temporal discretizations,*** subproblem is defined in the entire domain with vast majority of the degrees of freedom associated with the particular subdomain that it is responsible for and hence can be solved in parallel with other subproblems using an existing sequential solver without extensive *** algorithm is easy to implement and has low communication *** bounds of the parallel finite element approximate solutions are *** experiments are also given to demonstrate the effectiveness of the algorithm.

关键词： oseen equations finite element overlapping domain decomposition backward Euler scheme parallel algorithm

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oseen Coupling Method for the Exterior Flow Part Ⅰ:oseen Coupling Approximation

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Acta Mathematica Sinica,English Series 2000年第2期16卷 337-348页

作者： Yinnian He Kaitai Li College of Science,Xi’an Jiaotong University,Xi’an 710049,P.R.China

In this paper, we consider the bidimensional exterior unsteady Navier-Stokes equations with nonhomogeneous boundary conditions and present an oseen coupling problem which approximates the Navier-Stokes problem, obtained by coupling the Navier-Stokes equations in the inner region and the oseen equations in the outer region. Moreover, we prove the existence, uniqueness and the approximate accuracy of the weak solution of the oseen coupling equations.

关键词： Navier-Stokes equations oseen equations Nonhomogeneous boundary conditions

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FINITE ELEMENT NONLINEAR GALERKIN COUPLINGMETHOD FOR THE EXTERIOR STEADY NAVIER-STOKESPROBLEM

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Journal of Computational Mathematics 1999年第6期17卷 595-608页

作者： Yin-nian He Kai-tai Li Fu-hai Gao(College of Science, Xi’an Jiaotong University, Xi’an 710049, China) Xian Jiao Tong Univ Coll Sci Xian 710049 Peoples R China

In this paper we represent a new numerical method for solving the steady Navier-Stokes equations in three dimensional unbounded domain. The method consists in coupling the boundary integral and the finite element nonlinear Galerkin methods. An artificial smooth boundary is introduced seperating an interior inhomogeneous region from an exterior one. The Navier-Stokes equations in the exterior region are approximated by the oseen equations and the approximate solution is represented by an integral equation over the artificial boundary. Moreover, a finite element nonlinear Galerkin method is used to approximate the resulting variational problem. Finally, the existence and error estimates are derived.

关键词： Navier-Stokes equations oseen equations boundary integral finite element nonlinear Galerkin method

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THE APPROXIMATIONS OF THE EXACT BOUNDARY CONDITION AT AN ARTIFICIAL BOUNDARY FOR LINEARIZED INCOMPRESSIBLE VISCOUS FLOWS

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Journal of Computational Mathematics 1998年第3期16卷 239-256页

作者： Wei-zhu Bao (Department of Applied Mathematics, Tsinghua University, Beijing 100084, P.R. China) 清华大学应用数学系北京

We consider the linearized incompressible Navier-Stokes (oseen) equations in a flat channel. A sequence of approximations to the exact boundary condition at an artificial boundary is derived. Then the original problem is reduced to a boundary value problem in a bounded domain, which is well-posed. A finite element approximation on the bounded domain is given, furthermore the error estimate of the finite element approximation is obtained. Numerical example shows that our artificial boundary conditions are very effective.

关键词： oseen equations artificial boundary artificial boundary condition finite element approximation error estimate

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