Stability of the Ritz projection in weighted W

• Irene Drelichman ^[1] ; Ricardo G. Durán ^[2]
  1. [1] Universidad Nacional de La Plata

     Universidad Nacional de La Plata

     Argentina

     
  2. [2] Universidad de Buenos Aires

     Universidad de Buenos Aires

     Argentina

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 69, Nº. 1, 2026, págs. 21-24
• Idioma: inglés
• DOI: 10.33044/revuma.5001
• Enlaces
  • Texto completo
• Resumen

  • We prove stability in weighted W1,1 spaces for standard finite element approximations of the Poisson equation in convex polygonal or polyhedral domains, when the weight belongs to Muckenhoupt’s class A1 and the family of meshes is quasi-uniform.

• Referencias bibliográficas
  • S. C. Brenner and L. R. Scott, The mathematical theory of finite element methods, third ed., Texts in Applied Mathematics 15, Springer, New...
  • P. G. Ciarlet, The finite element method for elliptic problems, Classics in Applied Mathematics 40, Society for Industrial and Applied Mathematics...
  • A. Demlow, D. Leykekhman, A. H. Schatz, and L. B. Wahlbin, Best approximation property in the W1∞ norm for finite element methods on graded...
  • L. Diening, J. Rolfes, and A. J. Salgado, Pointwise gradient estimate of the Ritz projection, SIAM J. Numer. Anal. 62 no. 3 (2024), 1212–1225....
  • I. Drelichman, R. G. Durán, and I. Ojea, A weighted setting for the numerical approximation of the Poisson problem with singular sources,...
  • J. Guzmán, D. Leykekhman, J. Rossmann, and A. H. Schatz, Hölder estimates for Green's functions on convex polyhedral domains and their...
  • E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series 30, Princeton University Press,...