scholarly journals Numerical Computation of Brinkman Flow with Stable Mixed Element Method

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Xindong Li ◽  
Wenwen Xu
Keyword(s):  
Finite Element ◽  
Stokes Problem ◽  
Mixed Finite Element ◽  
Fluid Motion ◽  
Mixed Finite Element Method ◽  
Brinkman Equation ◽  
Finite Spaces ◽  
Perturbation Parameters ◽  
The Stability ◽  
Element Method

Herein, we discuss a mixed finite element method applied to the Brinkman equation of fluid motion in porous medium, which covers a field of situation from the Darcy equation to the Stokes problem associated with various perturbation parameters. The finite element based on staggered meshes is shown to be stable and effective with each case as the corresponding error estimates for both velocity and pressure are established. Finally, we present numerical examples confirming the theoretical analysis and the stability of the finite spaces approximation.

scholarly journals A Defect-Correction Mixed Finite Element Method for Stationary Conduction-Convection Problems

2011 ◽  
Vol 2011 ◽  
pp. 1-28 ◽  
Author(s):  
Zhiyong Si ◽  
Yinnian He
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Good Precision ◽  
Defect Correction ◽  
Viscosity Term ◽  
Correction Technique ◽  
The Stability ◽  
Element Method

A defect-correction mixed finite element method (MFEM) for solving the stationary conduction-convection problems in two-dimension is given. In this method, we solve the nonlinear equations with an added artificial viscosity term on a grid and correct this solution on the same grid using a linearized defect-correction technique. The stability is given and the error analysis inL2andH1-norm ofu,Tand theL2-norm ofpare derived. The theory analysis shows that our method is stable and has a good precision. Some numerical results are also given, which show that the defect-correction MFEM is highly efficient for the stationary conduction-convection problems.

Edge behaviour of the solution of the Stokes problem with applications to the finite-element method

2000 ◽  
Vol 130 (1) ◽  
pp. 107-140 ◽  
Author(s):  
J. M.-S. Lubuma ◽  
S. Nicaise
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Global Regularity ◽  
Stokes Problem ◽  
Mixed Finite Element ◽  
Weighted Sobolev Spaces ◽  
Regularity Result ◽  
Mixed Finite Element Method ◽  
Singular Functions ◽  
Element Method

The Stokes problem on a domain with edge singularities is considered. The decomposition of the solution into a regular part and blocks of singular functions is established. This, together with the tangential regularity of the solution, leads to a global regularity result in suitable weighted Sobolev spaces, the properties of which are investigated. The global regularity is exploited to generate an optimally convergent semi-discrete mesh refinement mixed finite-element method. In the particular case of a prismatic domain, the Fourier finite-element method, which is a fully discrete scheme, is implemented.

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