Finite element method for nonlocal problems of Kirchhoff-type in domains with moving boundary
This paper is devoted to the analysis of the finite element method for the mixed problem for the Kirchhoff nonlinear model given by the hyperbolic-parabolic equations in a bounded noncylindrical domain with moving boundaries. With the use of the coordinate transformation which fixes the boundaries,...
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| Format: | Article |
| Language: | English |
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Elsevier
2022-07-01
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| Series: | Scientific African |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2468227622001636 |
| _version_ | 1811242047598755840 |
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| author | M. Mbehou M.S. Daoussa Haggar P.M. Tchepmo Djomegni |
| author_facet | M. Mbehou M.S. Daoussa Haggar P.M. Tchepmo Djomegni |
| author_sort | M. Mbehou |
| collection | DOAJ |
| description | This paper is devoted to the analysis of the finite element method for the mixed problem for the Kirchhoff nonlinear model given by the hyperbolic-parabolic equations in a bounded noncylindrical domain with moving boundaries. With the use of the coordinate transformation which fixes the boundaries, the semidiscrete formulation is presented and the convergence and error bounds in the energy norm and for the first order derivative with respect to time in the L2-norm are established. In particular, the error in the energy norm and for the first order derivative with respect to time in the L2-norm is shown to converge with the optimal order O(hr) with respect to the mesh size h and the polynomial degree r≥1. To obtain the fully discrete solution, the generalized-α method is adapted to the semidiscrete formulation. The test problems used are designed to illustrate the behavior of the algorithms. Some numerical tests using Matlab are performed to confirm our theoretical findings. |
| first_indexed | 2024-04-12T13:45:08Z |
| format | Article |
| id | doaj.art-c6ab8426a5f44c14a2f91f6c87e7553d |
| institution | Directory Open Access Journal |
| issn | 2468-2276 |
| language | English |
| last_indexed | 2024-04-12T13:45:08Z |
| publishDate | 2022-07-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Scientific African |
| spelling | doaj.art-c6ab8426a5f44c14a2f91f6c87e7553d2022-12-22T03:30:42ZengElsevierScientific African2468-22762022-07-0116e01256Finite element method for nonlocal problems of Kirchhoff-type in domains with moving boundaryM. Mbehou0M.S. Daoussa Haggar1P.M. Tchepmo Djomegni2Corresponding author.; Department of Mathematics, University of Yaounde I, CameroonDepartment of Mathematics, University of Ndjamena, ChadSchool of Mathematical and Statistical Sciences, North West University, South AfricaThis paper is devoted to the analysis of the finite element method for the mixed problem for the Kirchhoff nonlinear model given by the hyperbolic-parabolic equations in a bounded noncylindrical domain with moving boundaries. With the use of the coordinate transformation which fixes the boundaries, the semidiscrete formulation is presented and the convergence and error bounds in the energy norm and for the first order derivative with respect to time in the L2-norm are established. In particular, the error in the energy norm and for the first order derivative with respect to time in the L2-norm is shown to converge with the optimal order O(hr) with respect to the mesh size h and the polynomial degree r≥1. To obtain the fully discrete solution, the generalized-α method is adapted to the semidiscrete formulation. The test problems used are designed to illustrate the behavior of the algorithms. Some numerical tests using Matlab are performed to confirm our theoretical findings.http://www.sciencedirect.com/science/article/pii/S246822762200163665N3065N1235K65Kirchhoff modelMoving boundariesNonlocal model |
| spellingShingle | M. Mbehou M.S. Daoussa Haggar P.M. Tchepmo Djomegni Finite element method for nonlocal problems of Kirchhoff-type in domains with moving boundary Scientific African 65N30 65N12 35K65 Kirchhoff model Moving boundaries Nonlocal model |
| title | Finite element method for nonlocal problems of Kirchhoff-type in domains with moving boundary |
| title_full | Finite element method for nonlocal problems of Kirchhoff-type in domains with moving boundary |
| title_fullStr | Finite element method for nonlocal problems of Kirchhoff-type in domains with moving boundary |
| title_full_unstemmed | Finite element method for nonlocal problems of Kirchhoff-type in domains with moving boundary |
| title_short | Finite element method for nonlocal problems of Kirchhoff-type in domains with moving boundary |
| title_sort | finite element method for nonlocal problems of kirchhoff type in domains with moving boundary |
| topic | 65N30 65N12 35K65 Kirchhoff model Moving boundaries Nonlocal model |
| url | http://www.sciencedirect.com/science/article/pii/S2468227622001636 |
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