scholarly journals Mixed Mortar Element Method forP1NC/P0Element and Its Multigrid Method for the Incompressible Stokes Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Yaqin Jiang ◽  
Jinru Chen
Keyword(s):  
Multigrid Method ◽  
Stokes Problem ◽  
Mesh Size ◽  
Optimal Error Estimate ◽  
Discrete Problem ◽  
Mixed Mortar ◽  
Mortar Element ◽  
Mortar Element Method ◽  
Theoretical Results ◽  
Element Method

We discuss a mortar-typeP1NC/P0element method for the incompressible Stokes problem. We prove the inf-sup condition and obtain the optimal error estimate. Meanwhile, we propose a𝒲-cycle multigrid for solving this discrete problem and prove the optimal convergence of the multigrid method, that is, the convergence rate is independent of the mesh size and mesh level. Finally, numerical experiments are presented to confirm our theoretical results.

scholarly journals Multigrid for the Wilson Mortar Element Method

2001 ◽  
Vol 1 (1) ◽  
pp. 99-112 ◽  
Author(s):  
Zhong-Ci Shi ◽  
Xuejun Xu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Discrete System ◽  
Multigrid Method ◽  
Nonconforming Element ◽  
Mortar Finite Element Method ◽  
Mortar Element ◽  
Wilson Nonconforming Element ◽  
Mortar Element Method ◽  
Element Method

AbstractIn this paper, a mortar finite element method is proposed for the Wilson nonconforming element. Multigrid method is used to solve the resulting discrete system.

scholarly journals An Oseen Two-Level Stabilized Mixed Finite-Element Method for the 2D/3D Stationary Navier-Stokes Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Aiwen Wang ◽  
Xin Zhao ◽  
Peihua Qin ◽  
Dongxiu Xie
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stokes Equations ◽  
Stokes Problem ◽  
Mesh Size ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Stabilized Finite Element ◽  
Stabilized Finite Element Method ◽  
Element Method

We investigate an Oseen two-level stabilized finite-element method based on the local pressure projection for the 2D/3D steady Navier-Stokes equations by the lowest order conforming finite-element pairs (i.e.,Q1−P0andP1−P0). Firstly, in contrast to other stabilized methods, they are parameter free, no calculation of higher-order derivatives and edge-based data structures, implemented at the element level with minimal cost. In addition, the Oseen two-level stabilized method involves solving one small nonlinear Navier-Stokes problem on the coarse mesh with mesh sizeH, a large general Stokes equation on the fine mesh with mesh sizeh=O(H)2. The Oseen two-level stabilized finite-element method provides an approximate solution (uh,ph) with the convergence rate of the same order as the usual stabilized finite-element solutions, which involves solving a large Navier-Stokes problem on a fine mesh with mesh sizeh. Therefore, the method presented in this paper can save a large amount of computational time. Finally, numerical tests confirm the theoretical results. Conclusion can be drawn that the Oseen two-level stabilized finite-element method is simple and efficient for solving the 2D/3D steady Navier-Stokes equations.

scholarly journals Unsteady Flow Calculation in a Cross-Flow Fan Using a Finite Element Method

1996 ◽  
Author(s):  
P. F. Bert ◽  
M. Pessiani ◽  
J. F. Combes ◽  
J. L. Kueny
Keyword(s):  
Finite Element ◽  
Unsteady Flow ◽  
Cross Flow ◽  
Doppler Velocity ◽  
Start Up ◽  
Large Vortex ◽  
Mortar Element ◽  
Cross Flow Fan ◽  
Mortar Element Method ◽  
Element Method

In order to predict rotor-stator interactions in hydraulic turbomachinery, a new multidomain method was implemented in a turbulent flow finite element code. The formulation is based on the mortar element method, extended to sliding meshes. It allows the coupling between several domains using nonconforming discretization on the interface. This method was used to study the unsteady flow in a cross-flow fan. Such fans are widely used in air-conditioning devices. They consist of a cylindrical rotor with forward curved blades, rotating in a housing. The air passes the blades twice at the inlet and the outlet of the impeller while a large vortex is noticeable inside the impeller which is located in the blading near the stabilizer. The numerical results are compared to Laser Doppler Velocity measurements and to steady calculations obtained by replacing the blades by a rotating force field. The unsteady calculation shows the formation of the vortex structure at the start-up and the periodic established flow after a few revolutions of the impeller.

Basics and some applications of the mortar element method

2005 ◽  
Vol 28 (2) ◽  
pp. 97-123 ◽  
Author(s):  
Christine Bernardi ◽  
Yvon Maday ◽  
Francesca Rapetti
Keyword(s):  
Mortar Element ◽  
Mortar Element Method ◽  
Element Method

Using hierarchic interpolation with mortar element method for electrical machines analysis

2005 ◽  
Vol 41 (5) ◽  
pp. 1472-1475 ◽  
Author(s):  
O.J. Antunes ◽  
J.P.A. Bastos ◽  
N. Sadowski ◽  
A. Razek ◽  
L. Santandrea ◽  
...  
Keyword(s):  
Electrical Machines ◽  
Mortar Element ◽  
Mortar Element Method ◽  
Element Method
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