Optimal convergence rates for the finite element approximation of the Sobolev constant

Ignat LI, Zuazua Iriondo E (2025)

Publication Language: English

Publication Status: Submitted

Publication Type: Unpublished / Preprint

Future Publication Type: Journal article

Publication year: 2025

Open Access Link: https://dcn.nat.fau.eu/wp-content/uploads/Sobolev-LE-10.04.25-final.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

Romanian Academy / Academia Română RO Romania (RO)

How to cite

APA:

Ignat, L.I., & Zuazua Iriondo, E. (2025). Optimal convergence rates for the finite element approximation of the Sobolev constant. (Unpublished, Submitted).

MLA:

Ignat, Liviu I., and Enrique Zuazua Iriondo. Optimal convergence rates for the finite element approximation of the Sobolev constant. Unpublished, Submitted. 2025.

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