Fully Discrete Finite Element Approximation for the Stabilized Gauge-Uzawa Method to Solve the Boussinesq Equations
The stabilized Gauge-Uzawa method (SGUM), which is a 2nd-order projection type algorithm used to solve Navier-Stokes equations, has been newly constructed in the work of Pyo, 2013. In this paper, we apply the SGUM to the evolution Boussinesq equations, which model the thermal driven motion of incomp...
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/372906 |
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| _version_ | 1832554857231286272 |
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| author | Jae-Hong Pyo |
| author_facet | Jae-Hong Pyo |
| author_sort | Jae-Hong Pyo |
| collection | DOAJ |
| description | The stabilized Gauge-Uzawa method (SGUM), which is a 2nd-order projection type algorithm used to solve Navier-Stokes equations, has been newly constructed in the work of Pyo, 2013. In this paper, we apply the SGUM to the evolution Boussinesq equations, which model the thermal driven motion of incompressible fluids. We prove that SGUM is unconditionally stable, and we perform error estimations on the fully discrete finite element space via variational approach for the velocity, pressure, and temperature, the three physical unknowns. We conclude with numerical tests to check accuracy and physically relevant numerical simulations, the Bénard convection problem and the thermal driven cavity flow. |
| format | Article |
| id | doaj-art-a2a9640e834f47af837a7b46f69c1a6a |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-a2a9640e834f47af837a7b46f69c1a6a2025-02-03T05:50:25ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/372906372906Fully Discrete Finite Element Approximation for the Stabilized Gauge-Uzawa Method to Solve the Boussinesq EquationsJae-Hong Pyo0Department of Mathematics, Kangwon National University, Chuncheon 200-701, Republic of KoreaThe stabilized Gauge-Uzawa method (SGUM), which is a 2nd-order projection type algorithm used to solve Navier-Stokes equations, has been newly constructed in the work of Pyo, 2013. In this paper, we apply the SGUM to the evolution Boussinesq equations, which model the thermal driven motion of incompressible fluids. We prove that SGUM is unconditionally stable, and we perform error estimations on the fully discrete finite element space via variational approach for the velocity, pressure, and temperature, the three physical unknowns. We conclude with numerical tests to check accuracy and physically relevant numerical simulations, the Bénard convection problem and the thermal driven cavity flow.http://dx.doi.org/10.1155/2013/372906 |
| spellingShingle | Jae-Hong Pyo Fully Discrete Finite Element Approximation for the Stabilized Gauge-Uzawa Method to Solve the Boussinesq Equations Journal of Applied Mathematics |
| title | Fully Discrete Finite Element Approximation for the Stabilized Gauge-Uzawa Method to Solve the Boussinesq Equations |
| title_full | Fully Discrete Finite Element Approximation for the Stabilized Gauge-Uzawa Method to Solve the Boussinesq Equations |
| title_fullStr | Fully Discrete Finite Element Approximation for the Stabilized Gauge-Uzawa Method to Solve the Boussinesq Equations |
| title_full_unstemmed | Fully Discrete Finite Element Approximation for the Stabilized Gauge-Uzawa Method to Solve the Boussinesq Equations |
| title_short | Fully Discrete Finite Element Approximation for the Stabilized Gauge-Uzawa Method to Solve the Boussinesq Equations |
| title_sort | fully discrete finite element approximation for the stabilized gauge uzawa method to solve the boussinesq equations |
| url | http://dx.doi.org/10.1155/2013/372906 |
| work_keys_str_mv | AT jaehongpyo fullydiscretefiniteelementapproximationforthestabilizedgaugeuzawamethodtosolvetheboussinesqequations |