$Stability of the Ritz projection in weighted $W^{1,1}$$

Stability of the Ritz projection in weighted $W^{1,1}$

We prove the stability in weighted $W^{1,1}$ spaces for standard finite element approximations of the Poisson equation in convex polygonal or polyhedral domains, when the weight belongs to Muckenhoupt's class $A_1$ and the family of meshes is quasi-uniform.

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Bibliographische Detailangaben
Veröffentlicht in:	arXiv.org 2024-03
Hauptverfasser:	Drelichman, Irene, Duran, Ricardo G
Format:	Artikel
Sprache:	eng
Schlagworte:	Poisson equation Stability
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	We prove the stability in weighted $W^{1,1}$ spaces for standard finite element approximations of the Poisson equation in convex polygonal or polyhedral domains, when the weight belongs to Muckenhoupt's class $A_1$ and the family of meshes is quasi-uniform.
ISSN:	2331-8422

Zusammenfassung:	We prove the stability in weighted \(W^{1,1}\) spaces for standard finite element approximations of the Poisson equation in convex polygonal or polyhedral domains, when the weight belongs to Muckenhoupt's class \(A_1\) and the family of meshes is quasi-uniform.
ISSN:	2331-8422

Stability of the Ritz projection in weighted \(W^{1,1}\)