From Finite Elements to Hybrid High-Order methods
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917942426337280 |
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| author | Di Pietro, Daniele A. Droniou, Jérôme |
| author_facet | Di Pietro, Daniele A. Droniou, Jérôme |
| contents | This document contains lecture notes from the Ph.D. course given at Scuola Superiore Meridionale by Daniele Di Pietro in February 2025. The goal of the course is to provide an overview of polytopal methods, focusing on the Hybrid High-Order (HHO) method. As a starting point, we study the Crouzeix-Raviart method for a pure diffusion equation, with particular focus on its stability. We then show that, switching to a fully discrete point of view, it is possible to generalize it first to polyhedral meshes and then to arbitrary order, leading to a method that belongs to the HHO family. A study of the stability and consistency of this method reveals the need for a stabilization term, for which we identify two key properties. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_00425 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From Finite Elements to Hybrid High-Order methods Di Pietro, Daniele A. Droniou, Jérôme Numerical Analysis 65N30, 65N12 This document contains lecture notes from the Ph.D. course given at Scuola Superiore Meridionale by Daniele Di Pietro in February 2025. The goal of the course is to provide an overview of polytopal methods, focusing on the Hybrid High-Order (HHO) method. As a starting point, we study the Crouzeix-Raviart method for a pure diffusion equation, with particular focus on its stability. We then show that, switching to a fully discrete point of view, it is possible to generalize it first to polyhedral meshes and then to arbitrary order, leading to a method that belongs to the HHO family. A study of the stability and consistency of this method reveals the need for a stabilization term, for which we identify two key properties. |
| title | From Finite Elements to Hybrid High-Order methods |
| topic | Numerical Analysis 65N30, 65N12 |
| url | https://arxiv.org/abs/2503.00425 |