Reconstructing algebraic functions from a nonconforming exponential weighted enriched finite element
The reconstruction of functions is a fundamental task in various applications, ranging from computer graphics to remote sensing. This paper addresses the challenge of function reconstruction in scenarios where, instead of pointwise function evaluations, only a set of integrals over specific lines is available. We propose a novel method based on a one-parameter family of weighted finite elements that incorporates exponential Hermite weight functions within bounded domains. Numerical experiments demonstrate that the proposed approach significantly improves computational efficiency and accuracy in function reconstruction compared to the classical Crouzeix–Raviart finite element.
Authors
- Allal Guessab (ORCID: https://orcid.org/0000-0001-8394-9155)
- Gradimir V. Milovanović (ORCID: https://orcid.org/0000-0002-3255-8127)
- Federico Nudo (ORCID: https://orcid.org/0000-0003-4418-3817)
- Francesco Dell’Accio (ORCID: https://orcid.org/0000-0003-4879-894X)
Institutions
- Centre National de la Recherche Scientifique (FR)
- Serbian Academy of Sciences and Arts (RS)
- University of Padua (IT)
- Université de Pau et des Pays de l'Adour (FR)
- University of Nis (RS)
- Laboratoire de Mathématiques et de leurs Applications (FR)
- Istituto per le Applicazioni del Calcolo Mauro Picone (IT)
- Civita (IT)
- National Research Council (IT)
- University of Calabria (IT)
Publication Details
- Journal
- Journal of Computational and Applied Mathematics
- Published
- 2025-02-28
- DOI
- https://doi.org/10.1016/j.cam.2025.116603
- Citations
- 2
- Primary Topic
- Advanced Numerical Methods in Computational Mathematics
- Type
- article
- Field-Weighted Citation Impact
- 2.67