Partial differential equations on domains presenting point singularities have always been of interest for applied mathematicians; this interest stems from the difficulty to prove regularity results for non-smooth domains, which has important consequences in the numerical solution of partial differential equations. In my thesis I address those consequences in the case of conforming and penalty finite element methods. The main results here contained concerns a priori error estimates for conforming and penalty finite element methods with respect to the energy norm, the $\mathcal{L}^2(\Omega)$ norm in both the standard and weighted setting.
| Identifer | oai:union.ndltd.org:kaust.edu.sa/oai:repository.kaust.edu.sa:10754/676498 |
| Date | 04 April 2022 |
| Creators | Zerbinati, Umberto |
| Contributors | Boffi, Daniele, Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division, Zampini, Stefano, Tzavaras, Athanasios, Tempone, Raul |
| Source Sets | King Abdullah University of Science and Technology |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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