A finite element method for a two-dimensional Pucci equation
A nonlinear least-squares finite element method for strong solutions of the Dirichlet boundary value problem of a two-dimensional Pucci equation on convex polygonal domains is investigated in this paper. We obtain a priori and a posteriori error estimates and present corroborating numerical results,...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-11-01
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| Series: | Comptes Rendus. Mécanique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.224/ |
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| _version_ | 1825206045525409792 |
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| author | Brenner, Susanne C. Sung, Li-yeng Tan, Zhiyu |
| author_facet | Brenner, Susanne C. Sung, Li-yeng Tan, Zhiyu |
| author_sort | Brenner, Susanne C. |
| collection | DOAJ |
| description | A nonlinear least-squares finite element method for strong solutions of the Dirichlet boundary value problem of a two-dimensional Pucci equation on convex polygonal domains is investigated in this paper. We obtain a priori and a posteriori error estimates and present corroborating numerical results, where the discrete nonsmooth and nonlinear optimization problems are solved by an active set method and an alternating direction method with multipliers. |
| format | Article |
| id | doaj-art-e6b480eda1dc4261a572dd30f05d6f12 |
| institution | Kabale University |
| issn | 1873-7234 |
| language | English |
| publishDate | 2023-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mécanique |
| spelling | doaj-art-e6b480eda1dc4261a572dd30f05d6f122025-02-07T13:46:20ZengAcadémie des sciencesComptes Rendus. Mécanique1873-72342023-11-01351S126127610.5802/crmeca.22410.5802/crmeca.224A finite element method for a two-dimensional Pucci equationBrenner, Susanne C.0Sung, Li-yeng1Tan, Zhiyu2Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, LA 70803, USADepartment of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, LA 70803, USACenter for Computation and Technology, Louisiana State University, Baton Rouge, LA 70803, USAA nonlinear least-squares finite element method for strong solutions of the Dirichlet boundary value problem of a two-dimensional Pucci equation on convex polygonal domains is investigated in this paper. We obtain a priori and a posteriori error estimates and present corroborating numerical results, where the discrete nonsmooth and nonlinear optimization problems are solved by an active set method and an alternating direction method with multipliers.https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.224/Pucci’s equationfinite element methodstrong solutiona priori and a posteriori error estimatesnonlinear least-squaresactive set methodADMM |
| spellingShingle | Brenner, Susanne C. Sung, Li-yeng Tan, Zhiyu A finite element method for a two-dimensional Pucci equation Comptes Rendus. Mécanique Pucci’s equation finite element method strong solution a priori and a posteriori error estimates nonlinear least-squares active set method ADMM |
| title | A finite element method for a two-dimensional Pucci equation |
| title_full | A finite element method for a two-dimensional Pucci equation |
| title_fullStr | A finite element method for a two-dimensional Pucci equation |
| title_full_unstemmed | A finite element method for a two-dimensional Pucci equation |
| title_short | A finite element method for a two-dimensional Pucci equation |
| title_sort | finite element method for a two dimensional pucci equation |
| topic | Pucci’s equation finite element method strong solution a priori and a posteriori error estimates nonlinear least-squares active set method ADMM |
| url | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.224/ |
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