Menghis Teweldebrhan, Bahlibi and Karátson, János and Korotov, S. (2025) Discrete maximum principles with computable mesh conditions for nonlinear elliptic finite element problems. APPLIED NUMERICAL MATHEMATICS, 210. pp. 222-244. ISSN 0168-9274
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Abstract
Discrete maximum principles are essential measures of the qualitative reliability of the given numerical method, therefore they have been in the focus of intense research, including nonlinear elliptic boundary value problems describing stationary states in many nonlinear processes. In this paper we consider a general class of nonlinear elliptic problems which covers various special cases and applications. We provide exactly computable conditions on the geometric characteristics of widely studied finite element shapes: triangles, tetrahedra, prisms and rectangles, and guarantee the validity of discrete maximum principles under these conditions.
| Item Type: | Article |
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| Additional Information: | Department of Applied Analysis and Computational Mathematics, Eötvös Loránd University, Hungary Department of Mathematics, Mai Nefhi College of Science, National Higher Education and Research Institute, Asmara, Eritrea Department of Applied Analysis and Computational Mathematics, HUN-REN–ELTE Numerical Analysis and Large Networks Research Group, Eötvös Loránd University, Hungary Department of Analysis and Operations Research, Budapest University of Technology and Economics, Hungary Division of Mathematics and Physics, UKK, Mälardalen University, Västerås, Sweden Export Date: 15 January 2025; Cited By: 0; Correspondence Address: J. Karátson; Department of Applied Analysis and Computational Mathematics, HUN-REN–ELTE Numerical Analysis and Large Networks Research Group, Eötvös Loránd University, Hungary; email: kajkaat@caesar.elte.hu; CODEN: ANMAE |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 24 Sep 2025 10:52 |
| Last Modified: | 24 Sep 2025 10:52 |
| URI: | https://real.mtak.hu/id/eprint/225141 |
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