Sufficient conditions for strong discrete maximum principles in finite element solutions of linear and semilinear elliptic equations
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911516703326208 |
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| author | Draganescu, Andrei Scott, L. Ridgway |
| author_facet | Draganescu, Andrei Scott, L. Ridgway |
| contents | We introduce a novel technique for proving global strong discrete maximum principles for finite element discretizations of linear and semilinear elliptic equations for cases when the common, matrix-based sufficient conditions are not satisfied. The basic argument consists of extending the strong form of discrete maximum principle from macroelements to the entire domain via a connectivity argument. The method is applied to discretizations of elliptic equations with certain pathological meshes, and to semilinear elliptic equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_00932 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sufficient conditions for strong discrete maximum principles in finite element solutions of linear and semilinear elliptic equations Draganescu, Andrei Scott, L. Ridgway Numerical Analysis 65N30 We introduce a novel technique for proving global strong discrete maximum principles for finite element discretizations of linear and semilinear elliptic equations for cases when the common, matrix-based sufficient conditions are not satisfied. The basic argument consists of extending the strong form of discrete maximum principle from macroelements to the entire domain via a connectivity argument. The method is applied to discretizations of elliptic equations with certain pathological meshes, and to semilinear elliptic equations. |
| title | Sufficient conditions for strong discrete maximum principles in finite element solutions of linear and semilinear elliptic equations |
| topic | Numerical Analysis 65N30 |
| url | https://arxiv.org/abs/2509.00932 |