A Hybrid High-Order Finite Element Method for a Nonlocal Nonlinear Problem of Kirchhoff Type
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914098463113216 |
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| author | Mallik, Gouranga |
| author_facet | Mallik, Gouranga |
| contents | In this article, we design and analyze a hybrid high-order (HHO) finite element approximation for the solution of a nonlocal nonlinear problem of Kirchhoff type. The HHO method involves arbitrary-order polynomial approximations on structured and unstructured polytopal meshes. We establish the existence of a unique discrete solution to the nonlocal nonlinear discrete problem. We derive an optimal-order error estimate in the discrete energy norm. The discrete system is solved using Newton's iterations on the sparse matrix system. We perform numerical tests to substantiate the theoretical results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_15574 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Hybrid High-Order Finite Element Method for a Nonlocal Nonlinear Problem of Kirchhoff Type Mallik, Gouranga Numerical Analysis In this article, we design and analyze a hybrid high-order (HHO) finite element approximation for the solution of a nonlocal nonlinear problem of Kirchhoff type. The HHO method involves arbitrary-order polynomial approximations on structured and unstructured polytopal meshes. We establish the existence of a unique discrete solution to the nonlocal nonlinear discrete problem. We derive an optimal-order error estimate in the discrete energy norm. The discrete system is solved using Newton's iterations on the sparse matrix system. We perform numerical tests to substantiate the theoretical results. |
| title | A Hybrid High-Order Finite Element Method for a Nonlocal Nonlinear Problem of Kirchhoff Type |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2510.15574 |