A pressure-robust divergence free finite element basis for the Stokes equations
This paper considered divergence-free basis methods to solve the viscous Stokes equations. A discrete divergence-free subspace was constructed to reduce the saddle point problem of the Stokes problem to a smaller-sized symmetric and positive definite system solely depending on the velocity component...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-10-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2024261 |
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| author | Jay Chu Xiaozhe Hu Lin Mu |
| author_facet | Jay Chu Xiaozhe Hu Lin Mu |
| author_sort | Jay Chu |
| collection | DOAJ |
| description | This paper considered divergence-free basis methods to solve the viscous Stokes equations. A discrete divergence-free subspace was constructed to reduce the saddle point problem of the Stokes problem to a smaller-sized symmetric and positive definite system solely depending on the velocity components. Then, the system could decouple the unknowns in velocity and pressure and solve them independently. However, such a scheme may not ensure an accurate numerical solution to the velocity. In order to obtain satisfactory accuracy, we used a velocity reconstruction technique to enhance the divergence-free scheme to achieve the desired pressure and viscosity robustness. Numerical results were presented to demonstrate the robustness and accuracy of this discrete divergence-free method. |
| format | Article |
| id | doaj-art-944ef65cd3594a9ebdb57d52d07a4df3 |
| institution | Kabale University |
| issn | 2688-1594 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj-art-944ef65cd3594a9ebdb57d52d07a4df32025-01-23T07:52:53ZengAIMS PressElectronic Research Archive2688-15942024-10-0132105633564810.3934/era.2024261A pressure-robust divergence free finite element basis for the Stokes equationsJay Chu0Xiaozhe Hu1Lin Mu2Departmant of Mathematics, National Tsing Hua University, TaiwanDepartment of Mathematics, Tufts University, Medford, MA 02155, USADepartment of Mathematics, University of Georgia, Athens, GA 30602, USAThis paper considered divergence-free basis methods to solve the viscous Stokes equations. A discrete divergence-free subspace was constructed to reduce the saddle point problem of the Stokes problem to a smaller-sized symmetric and positive definite system solely depending on the velocity components. Then, the system could decouple the unknowns in velocity and pressure and solve them independently. However, such a scheme may not ensure an accurate numerical solution to the velocity. In order to obtain satisfactory accuracy, we used a velocity reconstruction technique to enhance the divergence-free scheme to achieve the desired pressure and viscosity robustness. Numerical results were presented to demonstrate the robustness and accuracy of this discrete divergence-free method.https://www.aimspress.com/article/doi/10.3934/era.2024261finite element methodsthe viscous stokes equationsdivergence-free basispressure robustness |
| spellingShingle | Jay Chu Xiaozhe Hu Lin Mu A pressure-robust divergence free finite element basis for the Stokes equations Electronic Research Archive finite element methods the viscous stokes equations divergence-free basis pressure robustness |
| title | A pressure-robust divergence free finite element basis for the Stokes equations |
| title_full | A pressure-robust divergence free finite element basis for the Stokes equations |
| title_fullStr | A pressure-robust divergence free finite element basis for the Stokes equations |
| title_full_unstemmed | A pressure-robust divergence free finite element basis for the Stokes equations |
| title_short | A pressure-robust divergence free finite element basis for the Stokes equations |
| title_sort | pressure robust divergence free finite element basis for the stokes equations |
| topic | finite element methods the viscous stokes equations divergence-free basis pressure robustness |
| url | https://www.aimspress.com/article/doi/10.3934/era.2024261 |
| work_keys_str_mv | AT jaychu apressurerobustdivergencefreefiniteelementbasisforthestokesequations AT xiaozhehu apressurerobustdivergencefreefiniteelementbasisforthestokesequations AT linmu apressurerobustdivergencefreefiniteelementbasisforthestokesequations AT jaychu pressurerobustdivergencefreefiniteelementbasisforthestokesequations AT xiaozhehu pressurerobustdivergencefreefiniteelementbasisforthestokesequations AT linmu pressurerobustdivergencefreefiniteelementbasisforthestokesequations |