Numerical solution and errors analysis of iterative method for a nonlinear plate bending problem
This paper uses the HCT finite element method and mesh adaptation technology to solve the nonlinear plate bending problem and conducts error analysis on the iterative method, including a priori and a posteriori error estimates. Our investigation exploits Hermite finite elements such as BELL and HSIE...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-05-01
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| Series: | Results in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590037425000408 |
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| author | Akakpo Amoussou Wilfried Houédanou Koffi Wilfrid |
| author_facet | Akakpo Amoussou Wilfried Houédanou Koffi Wilfrid |
| author_sort | Akakpo Amoussou Wilfried |
| collection | DOAJ |
| description | This paper uses the HCT finite element method and mesh adaptation technology to solve the nonlinear plate bending problem and conducts error analysis on the iterative method, including a priori and a posteriori error estimates. Our investigation exploits Hermite finite elements such as BELL and HSIEH-CLOUGH-TOCHER (HCT) triangles for conforming finite element discretization. We use an iterative resolution algorithm to linearize the associated discrete problem and study the convergence of this algorithm towards the solution of the approximate problem. An optimal a priori error estimation has been established. We construct a posteriori error indicators by distinguishing between discretization and linearization errors and prove their reliability and optimality. A numerical test is carried out and the results obtained confirm those established theoretically. |
| format | Article |
| id | doaj-art-1267c7a712ea4b8ea536c4d741b68ced |
| institution | DOAJ |
| issn | 2590-0374 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Applied Mathematics |
| spelling | doaj-art-1267c7a712ea4b8ea536c4d741b68ced2025-08-20T03:10:27ZengElsevierResults in Applied Mathematics2590-03742025-05-012610057610.1016/j.rinam.2025.100576Numerical solution and errors analysis of iterative method for a nonlinear plate bending problemAkakpo Amoussou Wilfried0Houédanou Koffi Wilfrid1Institut de Mathématiques et de Sciences Physiques, Université d’Abomey-Calavi (UAC), Republic of BeninDépartement de Mathématiques, Facultés des Sciences et Techniques, Université d’Abomey-Calavi (UAC), Republic of Benin; Corresponding author.This paper uses the HCT finite element method and mesh adaptation technology to solve the nonlinear plate bending problem and conducts error analysis on the iterative method, including a priori and a posteriori error estimates. Our investigation exploits Hermite finite elements such as BELL and HSIEH-CLOUGH-TOCHER (HCT) triangles for conforming finite element discretization. We use an iterative resolution algorithm to linearize the associated discrete problem and study the convergence of this algorithm towards the solution of the approximate problem. An optimal a priori error estimation has been established. We construct a posteriori error indicators by distinguishing between discretization and linearization errors and prove their reliability and optimality. A numerical test is carried out and the results obtained confirm those established theoretically.http://www.sciencedirect.com/science/article/pii/S2590037425000408Plate bending problemIsotropic discretizationBELL and HCT trianglesIterative methodA priori error estimationA posteriori error estimation |
| spellingShingle | Akakpo Amoussou Wilfried Houédanou Koffi Wilfrid Numerical solution and errors analysis of iterative method for a nonlinear plate bending problem Results in Applied Mathematics Plate bending problem Isotropic discretization BELL and HCT triangles Iterative method A priori error estimation A posteriori error estimation |
| title | Numerical solution and errors analysis of iterative method for a nonlinear plate bending problem |
| title_full | Numerical solution and errors analysis of iterative method for a nonlinear plate bending problem |
| title_fullStr | Numerical solution and errors analysis of iterative method for a nonlinear plate bending problem |
| title_full_unstemmed | Numerical solution and errors analysis of iterative method for a nonlinear plate bending problem |
| title_short | Numerical solution and errors analysis of iterative method for a nonlinear plate bending problem |
| title_sort | numerical solution and errors analysis of iterative method for a nonlinear plate bending problem |
| topic | Plate bending problem Isotropic discretization BELL and HCT triangles Iterative method A priori error estimation A posteriori error estimation |
| url | http://www.sciencedirect.com/science/article/pii/S2590037425000408 |
| work_keys_str_mv | AT akakpoamoussouwilfried numericalsolutionanderrorsanalysisofiterativemethodforanonlinearplatebendingproblem AT houedanoukoffiwilfrid numericalsolutionanderrorsanalysisofiterativemethodforanonlinearplatebendingproblem |