Open Access
Issue
ESAIM: M2AN
Volume 59, Number 2, March-April 2025
Page(s) 1095 - 1112
DOI https://doi.org/10.1051/m2an/2025019
Published online 08 April 2025
  1. J.W. Barrett, Finite element approximation of a non-Lipschitz nonlinear eigenvalue problem. RAIRO Modél. Math. Anal. Numér. 26 (1992) 627–656. [MathSciNet] [Google Scholar]
  2. J.W. Barrett and R.M. Shanahan, Finite element approximation of a model reaction-diffusion problem with a non-Lipschitz nonlinearity. Numer. Math. 59 (1991) 217–242. [CrossRef] [MathSciNet] [Google Scholar]
  3. S.C. Brenner and L. Ridgway Scott, The Mathematical Theory of Finite Element Methods. Vol. 15 of Texts in Applied Mathematics, 3rd edition. Springer, New York (2008). [CrossRef] [Google Scholar]
  4. E. Casas, Boundary control of semilinear elliptic equations with pointwise state constraints. SIAM J. Control Optim. 31 (1993) 993–1006. [CrossRef] [MathSciNet] [Google Scholar]
  5. E. Casas and M. Mateos, Uniform convergence of the FEM. Applications to state constrained control problems. Comput. Appl. Math. 21 (2002) 67–100. [MathSciNet] [Google Scholar]
  6. C. Christof, Optimal control of semilinear elliptic partial differential equations with non-lipschitzian nonlinearities. Preprint arXiv:2406.03110 (2024). [Google Scholar]
  7. J. Frehse and R. Rannacher, Eine L1-Fehlerabsch¨atzung für diskrete Grundlösungen in der Methode der finiten Elemente, in Finite Elemente (Tagung, Inst. Angew. Math., Univ. Bonn, Bonn, 1975). Vol. 89 of Bonner Math. Schriften. Universit¨at Bonn, Institut für Angewandte Mathematik, Bonn (1976) 92–114. [Google Scholar]
  8. D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order. Classics in Mathematics. Springer-Verlag, Berlin (2001). Reprint of the 1998 edition. [CrossRef] [Google Scholar]
  9. P. Grisvard, Elliptic Problems in Nonsmooth Domains. Vol. 24 of Monographs and Studies in Mathematics. Pitman (Advanced Publishing Program), Boston, MA (1985). [Google Scholar]
  10. J. Guzmán, D. Leykekhman, J. Rossmann and A.H. Schatz, Hölder estimates for Green’s functions on convex polyhedral domains and their applications to finite element methods. Numer. Math. 112 (2009) 221–243. [Google Scholar]
  11. D. Hafemeyer, C. Kahle and J. Pfefferer, Finite element error estimates in L2 for regularized discrete approximations to the obstacle problem. Numer. Math. 144 (2020) 133–156. [CrossRef] [MathSciNet] [Google Scholar]
  12. D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and their Applications. Vol. 31 of Classics in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2000). Reprint of the 1980 original. [Google Scholar]
  13. P. Knabner and R. Rannacher, A priori error analysis for the Galerkin finite element semi-discretization of a parabolic system with non-Lipschitzian nonlinearity. Vietnam J. Math. 45 (2017) 179–198. [CrossRef] [MathSciNet] [Google Scholar]
  14. D. Leykekhman and B. Vexler, Finite element pointwise results on convex polyhedral domains. SIAM J. Numer. Anal. 54 (2016) 561–587. [Google Scholar]
  15. J.A. Nitsche and A.H. Schatz, Interior estimates for Ritz–Galerkin methods. Math. Comput. 28 (1974) 937–958. [CrossRef] [Google Scholar]
  16. R.H. Nochetto, Sharp L-error estimates for semilinear elliptic problems with free boundaries. Numer. Math. 54 (1988) 243–255. [Google Scholar]
  17. M. Růžička, Nichtlineare Funktionalanalysis. Masterclass, 2nd edition. Springer Spektrum Berlin, Heidelberg (2020). [Google Scholar]
  18. A.H. Schatz and L.B. Wahlbin, Interior maximum norm estimates for finite element methods. Math. Comput. 31 (1977) 414–442. [Google Scholar]
  19. F. Tröltzsch, Optimal Control of Partial Differential Equations: Theory, Methods and Applications. Vol. 112 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI (2010). Translated from the 2005 German original by Jürgen Sprekels. [CrossRef] [Google Scholar]
  20. E. Zeidler, Nonlinear Functional Analysis and its Applications. II/B. Springer-Verlag, New York (1990). Nonlinear monotone operators. Translated from the German by the author and Leo F. Boron. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you