EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 59 / No 4 (July-August 2025) ESAIM: M2AN, 59 4 (2025) 1937-1972 References
Open Access
Issue
ESAIM: M2AN
Volume 59, Number 4, July-August 2025
Page(s) 1937 - 1972
DOI https://doi.org/10.1051/m2an/2025027
Published online 17 July 2025
  1. G. Akrivis, C. Makridakis and R.H. Nochetto, Optimal order a posteriori error estimates for a class of Runge-Kutta and Galerkin methods. Numer. Math. 114 (2009) 133–160. [Google Scholar]
  2. R.E. Bank and H. Yserentant, On the H1-stability of the L2-projection onto finite element spaces. Numer. Math. 126 (2014) 361–381. [Google Scholar]
  3. C. Bernardi and E. Süli, Time and space adaptivity for the second-order wave equation. Math. Models Meth. Appl. Sci. 12 (2005) 199–225. [Google Scholar]
  4. P. Bignardi and A. Moiola, A space-time continuous and coercive formulation for the wave equation. Preprint arXiv:2312.07268 (2023). [Google Scholar]
  5. T. Chaumont-Frelet, Asymptotically constant-free and polynomial-degree-robust a posteriori estimates for space discretizations of the wave equation. SIAM J. Sci. Comput. 45 (2023) A1591–A1620. [Google Scholar]
  6. M. Dauge, Elliptic Boundary Value Problems on Corner Domains. Lecture Notes in Mathematics. Vol. 1341. Springer-Verlag, Berlin (1988). [Google Scholar]
  7. A. Ern and J.-L. Guermond, Finite Elements I: Approximation and Interpolation. Texts in Applied Mathematics. Vol. 72. Springer Nature, Cham, Switzerland (2021). [Google Scholar]
  8. A. Ern and M. Vohralík, Polynomial-degree-robust a posteriori estimates in a unified setting for conforming, non-conforming, discontinuous Galerkin, and mixed discretizations. SIAM J. Numer. Anal. 53 (2015) 1058–1081. [Google Scholar]
  9. A. Ern, I. Smears and M. Vohralík, Guaranteed, locally space-time efficient, and polynomial-degree robust a posteri- ori error estimates for high-order discretizations of parabolic problems. SIAM J. Numer. Anal. 55 (2017) 2811–2834. [Google Scholar]
  10. T. Führer, R. González and M. Karkulik, Well-posedness of first-order acoustic wave equations and space-time finite element approximation. Preprint arXiv:2311.10536 (2023). [Google Scholar]
  11. F.D. Gaspoz, C.-J. Heine and K.G. Siebert, Optimal grading of the newest vertex bisection and H1-stability of the L2-projection. IMA J. Numer. Anal. 36 (2016) 1217–1241. [Google Scholar]
  12. E.H. Georgoulis, O. Lakkis and C. Makridakis, A posteriori L∞(L2)-error bounds for finite element approximations to the wave equation. IMA J. Numer. Anal. 33 (2013) 1245–1264. [Google Scholar]
  13. E.H. Georgoulis, O. Lakkis, C. Makridakis and J.M. Virtanen, A posteriori error estimates for leap-frog and cosine methods for second order evolution problems. SIAM J. Numer. Anal. 54 (2016) 120–136. [Google Scholar]
  14. H. Gimperlein, C. Özdemir, D. Stark and E.P. Stephan, A residual a posteriori error estimate for the time-domain boundary element method. Numer. Math. 146 (2020) 239–280. [Google Scholar]
  15. O. Gorynina, A. Lozinski and M. Picasso, Time and space adaptivity of the wave equation discretized in time by a second-order scheme. IMA J. Numer. Anal. 39 (2019) 1672–1705. [Google Scholar]
  16. M. Grote, O. Lakkis and C. Santos, A posteriori error estimates for the wave equation with mesh change in the leapfrog method. Preprint arXiv:2411.16933 (2024). [Google Scholar]
  17. D. Hoonhout, R. Löscher, O. Steinbach and C. Urzúa-Torres, Stable least-squares space-time boundary element methods for the wave equation. arXiv:2312.12547 (2023). [Google Scholar]
  18. P. Joly, Variational methods for time-dependent wave propagation problems, in Topics in Computational Wave Propagation. Lect. Notes Comput. Sci. Eng. Vol. 31. Springer, Berlin (2003) 201–264. [Google Scholar]
  19. O.A. Karakashian and F. Pascal, A posteriori error estimates for a discontinuous Galerkin approximation of second-order elliptic problems. SIAM J. Numer. Anal. 41 (2003) 2374–2399. [Google Scholar]
  20. C. Makridakis and R.H. Nochetto, Elliptic reconstruction and a posteriori error estimates for parabolic problems. SIAM J. Numer. Anal. 41 (2003) 1585–1594. [Google Scholar]
  21. R.D. Skeel, Variable step size destabilizes the Störmer/leapfrog/Verlet method. BIT 33 (1993) 172–175. [Google Scholar]
  22. R. Verfürth, A posteriori error estimates for finite element discretizations of the heat equation. Calcolo 40 (2003) 195–212. [CrossRef] [MathSciNet] [Google Scholar]
  23. R. Verfürth, A Posteriori Error Estimation Techniques for Finite Element Methods. Oxford Science Publications (2013). [Google Scholar]
  24. M. Zank, Inf-sup stable space-time methods for time-dependent partial differential equations. Ph.D. thesis, Technische Universit¨at Graz (2019). [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