Optimal convergence rates for the finite element approximation of the Sobolev constant
Ignat LI, Zuazua E (2026)
Publication Language: English
Publication Status: Accepted
Publication Type: Unpublished / Preprint
Future Publication Type: Journal article
Publication year: 2026
Publisher: Found. Comput. Math.
Open Access Link: https://dcn.nat.fau.eu/wp-content/uploads/Sobolev-24.05.26.pdf
Abstract
We establish optimal convergence rates for the P1 finite element approximation of the Sobolev constant in arbitrary dimensions N ≥ 2 and for Lebesgue exponents 1 < p < N. Our analysis relies on a refined study of the Sobolev deficit in suitable quasi-norms, which have been introduced and utilized in the context of finite element approximations of the p- Laplacian. The proof further involves sharp estimates for the finite element approximation of Sobolev minimizers.
Authors with CRIS profile
Enrique Zuazua Iriondo
Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)
Involved external institutions
Romania (RO)How to cite
APA:
Ignat, L.I., & Zuazua, E. (2026). Optimal convergence rates for the finite element approximation of the Sobolev constant. (Unpublished, Accepted).
MLA:
Ignat, Liviu I., and Enrique Zuazua. Optimal convergence rates for the finite element approximation of the Sobolev constant. Unpublished, Accepted. 2026.
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