Stability Analysis of the Crank-Nicolson Finite Element Method for the Navier-Stokes Equations Driven by Slip Boundary Conditions
This paper is devoted to the study of numerical approximation for a class of two-dimensional Navier-Stokes equations with slip boundary conditions of friction type. The objective is to establish the well-posedness and stability of the numerical scheme in L2-norm and H1-norm for all positive time usi...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/7742867 |
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| author | M. Mbehou M. S. Daoussa Haggar H. Olei Tahar |
| author_facet | M. Mbehou M. S. Daoussa Haggar H. Olei Tahar |
| author_sort | M. Mbehou |
| collection | DOAJ |
| description | This paper is devoted to the study of numerical approximation for a class of two-dimensional Navier-Stokes equations with slip boundary conditions of friction type. The objective is to establish the well-posedness and stability of the numerical scheme in L2-norm and H1-norm for all positive time using the Crank-Nicholson scheme in time and the finite element approximation in space. The resulting variational structure dealing with is in the form of inequality, and obtaining H1-estimate is more involved because of the presence of the nondifferentiable term appearing at the boundary where slip occurs. We prove that the numerical scheme is stable in L2 and H1-norms with the aid of different versions of discrete Grownwall lemmas, under a CFL-type condition. Finally, some numerical simulations are presented to illustrate our theoretical analysis. |
| format | Article |
| id | doaj-art-fe8891c606d545aabf0b7c4e1e4dfc85 |
| institution | Kabale University |
| issn | 1687-0042 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-fe8891c606d545aabf0b7c4e1e4dfc852025-02-03T06:05:54ZengWileyJournal of Applied Mathematics1687-00422022-01-01202210.1155/2022/7742867Stability Analysis of the Crank-Nicolson Finite Element Method for the Navier-Stokes Equations Driven by Slip Boundary ConditionsM. Mbehou0M. S. Daoussa Haggar1H. Olei Tahar2Department of MathematicsDepartment of MathematicsDepartment of MathematicsThis paper is devoted to the study of numerical approximation for a class of two-dimensional Navier-Stokes equations with slip boundary conditions of friction type. The objective is to establish the well-posedness and stability of the numerical scheme in L2-norm and H1-norm for all positive time using the Crank-Nicholson scheme in time and the finite element approximation in space. The resulting variational structure dealing with is in the form of inequality, and obtaining H1-estimate is more involved because of the presence of the nondifferentiable term appearing at the boundary where slip occurs. We prove that the numerical scheme is stable in L2 and H1-norms with the aid of different versions of discrete Grownwall lemmas, under a CFL-type condition. Finally, some numerical simulations are presented to illustrate our theoretical analysis.http://dx.doi.org/10.1155/2022/7742867 |
| spellingShingle | M. Mbehou M. S. Daoussa Haggar H. Olei Tahar Stability Analysis of the Crank-Nicolson Finite Element Method for the Navier-Stokes Equations Driven by Slip Boundary Conditions Journal of Applied Mathematics |
| title | Stability Analysis of the Crank-Nicolson Finite Element Method for the Navier-Stokes Equations Driven by Slip Boundary Conditions |
| title_full | Stability Analysis of the Crank-Nicolson Finite Element Method for the Navier-Stokes Equations Driven by Slip Boundary Conditions |
| title_fullStr | Stability Analysis of the Crank-Nicolson Finite Element Method for the Navier-Stokes Equations Driven by Slip Boundary Conditions |
| title_full_unstemmed | Stability Analysis of the Crank-Nicolson Finite Element Method for the Navier-Stokes Equations Driven by Slip Boundary Conditions |
| title_short | Stability Analysis of the Crank-Nicolson Finite Element Method for the Navier-Stokes Equations Driven by Slip Boundary Conditions |
| title_sort | stability analysis of the crank nicolson finite element method for the navier stokes equations driven by slip boundary conditions |
| url | http://dx.doi.org/10.1155/2022/7742867 |
| work_keys_str_mv | AT mmbehou stabilityanalysisofthecranknicolsonfiniteelementmethodforthenavierstokesequationsdrivenbyslipboundaryconditions AT msdaoussahaggar stabilityanalysisofthecranknicolsonfiniteelementmethodforthenavierstokesequationsdrivenbyslipboundaryconditions AT holeitahar stabilityanalysisofthecranknicolsonfiniteelementmethodforthenavierstokesequationsdrivenbyslipboundaryconditions |