Open Access
Volume 55, Number 6, November-December 2021
Page(s) 2759 - 2784
Published online 25 November 2021
  1. M. Ainsworth, A posteriori error estimation for discontinuous Galerkin finite element approximation. SIAM J. Numer. Anal. 45 (2007) 1777–1798. [CrossRef] [MathSciNet] [Google Scholar]
  2. M. Ainsworth and R. Rankin, Fully computable bounds for the error in nonconforming finite element approximations of arbitrary order on triangular elements. SIAM J. Numer. Anal. 46 (2008) 3207–3232. [CrossRef] [MathSciNet] [Google Scholar]
  3. M. Ainsworth and O.J. Tinsley, A Posteriori Error Estimation in Finite Element Analysis, Vol 37. John Wiley & Sons (2011). [Google Scholar]
  4. S. Badia, F. Verdugo and A.F. Martn, The aggregated unfitted finite element method for elliptic problems. Comput. Methods Appl. Mech. Eng. 336 (2018) 533–553. [CrossRef] [Google Scholar]
  5. J.W. Barrett and C.M. Elliott, A finite-element method for solving elliptic equations with Neumann data on a curved boundary using unfitted meshes. IMA J. Numer. Anal. 4 (1984) 309–325. [CrossRef] [MathSciNet] [Google Scholar]
  6. P. Bastian and B. Rivière, Superconvergence and H(div) projection for discontinuous Galerkin methods. Int. J. Numer. Methods Fluids 42 (2003) 1043–1057. [CrossRef] [Google Scholar]
  7. R. Becker, D. Capatina and R. Luce, Local flux reconstructions for standard finite element methods on triangular meshes. SIAM J. Numer. Anal. 54 (2016) 2684–2706. [Google Scholar]
  8. S. Bertoluzza, M. Ismail and B. Maury, The fat boundary method: semi-discrete scheme and some numerical experiments. In: Domain Decomposition Methods in Science and Engineering. Vol. 40 of Lect. Notes Comput. Sci. Eng. Springer, Berlin (2005) 513–520. [CrossRef] [Google Scholar]
  9. D. Boffi, F. Brezzi and M. Fortin, Mixed Finite Element Methods and Applications, Vol 44. Springer (2013). [CrossRef] [Google Scholar]
  10. D. Braess, V. Pillwein and J. Schöberl, Equilibrated residual error estimates are p-robust. Comput. Methods Appl. Mech. Eng. 198 (2009) 1189–1197. [Google Scholar]
  11. D. Braess, T. Fraunholz and R.H. Hoppe, An equilibrated a posteriori error estimator for the interior penalty discontinuous Galerkin method. SIAM J. Numer. Anal. 52 (2014) 2121–2136. [CrossRef] [MathSciNet] [Google Scholar]
  12. E. Burman, Ghost penalty. C. R. Math. Acad. Sci. Paris 348 (2010) 1217–1220. [CrossRef] [MathSciNet] [Google Scholar]
  13. E. Burman and A. Ern, An unfitted hybrid high-order method for elliptic interface problems. SIAM J. Numer. Anal. 56 (2018) 1525–1546. [CrossRef] [MathSciNet] [Google Scholar]
  14. E. Burman and P. Hansbo, Fictitious domain finite element methods using cut elements: I. A stabilized Lagrange multiplier method. Comput. Methods Appl. Mech. Eng. 199 (2010) 2680–2686. [CrossRef] [Google Scholar]
  15. E. Burman and P. Hansbo, Fictitious domain finite element methods using cut elements: II. A stabilized Nitsche method. Appl. Numer. Math. 62 (2012) 328–341. [Google Scholar]
  16. E. Burman, P. Hansbo and M.G. Larson, A cut finite element method with boundary value correction. Math. Comput. 87 (2018) 633–657. [Google Scholar]
  17. E. Burman, C. He and M.G. Larson, A posteriori error estimates with boundary correction for a cut finite element method. IMA J. Numer. Anal. (2020) draa085. [Google Scholar]
  18. Z. Cai and S. Zhang, Robust equilibrated residual error estimator for diffusion problems: conforming elements. SIAM J. Numer. Anal. 50 (2012) 151–170. [CrossRef] [MathSciNet] [Google Scholar]
  19. Z. Cai, C. He and S. Zhang, Residual-based a posteriori error estimate for interface problems: nonconforming linear elements. Math. Comput. 86 (2017) 617–636. [Google Scholar]
  20. Z. Cai, C. He and S. Zhang, Generalized Prager-Synge identity and robust equilibrated error estimators for discontinuous elements. J. Comput. Appl. Math. 398 (2021) 11673. [Google Scholar]
  21. D.A. Di Pietro and A. Ern, Mathematical aspects of discontinuous Galerkin methods. In: Vol. 69 of Mathématiques & Applications (Berlin) [Mathematics & Applications]. Springer, Heidelberg (2012). [Google Scholar]
  22. P. Di Stolfo, A. Rademacher and A. Schröder, Dual weighted residual error estimation for the finite cell method. J. Numer. Math. 27 (2019) 101–122. [CrossRef] [MathSciNet] [Google Scholar]
  23. W. Dörfler, A convergent adaptive algorithm for Poisson’s equation. SIAM J. Numer. Anal. 33 (1996) 1106–1124. [Google Scholar]
  24. A. Ern and M. Vohralk, Polynomial-degree-robust a posteriori estimates in a unified setting for conforming, nonconforming, discontinuous Galerkin, and mixed discretizations. SIAM J. Numer. Anal. 53 (2015) 1058–1081. [Google Scholar]
  25. A. Ern, S. Nicaise and M. Vohralk, An accurate H(div) flux reconstruction for discontinuous Galerkin approximations of elliptic problems. C. R. Math. 345 (2007) 709–712. [CrossRef] [MathSciNet] [Google Scholar]
  26. D. Estep, M. Pernice, S. Tavener and H. Wang, A posteriori error analysis for a cut cell finite volume method. Comput. Methods Appl. Mech. Eng. 200 (2011) 2768–2781. [CrossRef] [Google Scholar]
  27. R. Franke, A critical comparison of some methods for interpolation of scattered data, Tech. Report, Navel Postgraduate School, Monterey, CA (1979). [Google Scholar]
  28. R. Glowinski and T.-W. Pan, Error estimates for fictitious domain/penalty/finite element methods. Calcolo 29 (1992) 125–141. [CrossRef] [MathSciNet] [Google Scholar]
  29. P. Grisvard, Elliptic problems in nonsmooth domains. In: Vol. 69 of Classics in Applied Mathematics. Reprint of the 1985 original [MR0775683], With a foreword by Susanne C. Brenner. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2011). [Google Scholar]
  30. A. Hansbo and P. Hansbo, An unfitted finite element method, based on Nitsche’s method, for elliptic interface problems. Comput. Methods Appl. Mech. Eng. 191 (2002) 5537–5552. [Google Scholar]
  31. J. Haslinger and Y. Renard, A new fictitious domain approach inspired by the extended finite element method. SIAM J. Numer. Anal. 47 (2009) 1474–1499. [Google Scholar]
  32. P. Huang, H. Wu and Y. Xiao, An unfitted interface penalty finite element method for elliptic interface problems. Comput. Methods Appl. Mech. Eng. 323 (2017) 439–460. [CrossRef] [Google Scholar]
  33. A. Johansson and M.G. Larson, A high order discontinuous Galerkin Nitsche method for elliptic problems with fictitious boundary. Numer. Math. 123 (2013) 607–628. [CrossRef] [MathSciNet] [Google Scholar]
  34. K.-Y. Kim, Flux reconstruction for the p2 nonconforming finite element method with application to a posteriori error estimation. Appl. Numer. Math. 62 (2012) 1701–1717. [CrossRef] [MathSciNet] [Google Scholar]
  35. L.D. Marini, An inexpensive method for the evaluation of the solution of the lowest order Raviart-Thomas mixed method. SIAM J. Numer. Anal. 22 (1985) 493–496. [CrossRef] [MathSciNet] [Google Scholar]
  36. A. Massing, M.G. Larson, A. Logg and M.E. Rognes, A stabilized Nitsche fictitious domain method for the Stokes problem. J. Sci. Comput. 61 (2014) 604–628. [Google Scholar]
  37. J. Nitsche, Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. Abh. Math. Sem. Univ. Hamburg 36 (1971) 9–15. Collection of articles dedicated to Lothar Collatz on his sixtieth birthday. [Google Scholar]
  38. L.H. Odsæter, M.F. Wheeler, T. Kvamsdal and M.G. Larson, Postprocessing of non-conservative flux for compatibility with transport in heterogeneous media. Comput. Methods Appl. Mech. Eng. 315 (2017) 799–830. [CrossRef] [Google Scholar]
  39. H. Sun, D. Schillinger and S. Yuan, Implicit a posteriori error estimation in cut finite elements. Comput. Mech. 65 (2020) 967–988. [CrossRef] [MathSciNet] [Google Scholar]
  40. R. Verfürth, A posteriori error estimation and adaptive mesh-refinement techniques. J. Comput. Appl. Math. 50 (1994) 67–83. [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