Open Access
| Issue |
ESAIM: M2AN
Volume 60, Number 3, May-June 2026
|
|
|---|---|---|
| Page(s) | 1269 - 1295 | |
| DOI | https://doi.org/10.1051/m2an/2026036 | |
| Published online | 01 June 2026 | |
- M. Ainsworth, A a posteriori error estimation for discontinuous Galerkin finite element approximation. SIAM J. Numer. Anal. 45 (2007) 1777–1798. [CrossRef] [MathSciNet] [Google Scholar]
- 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]
- A. Bonito, R.A. Devore and R.H. Nochetto, Adaptive finite element methods for elliptic problems with discontinuous coefficients. SIAM J. Numer. Anal. 51 (2013) 3106–3134. [Google Scholar]
- D. Braess and J. Schöberl, Equilibrated residual error estimator for edge elements. Math. Comput. 77 (2008) 651–672. [Google Scholar]
- 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]
- F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Method. Springer-Verlag, New York (1991). [Google Scholar]
- 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]
- E. Burman, S. Claus, P. Hansbo, M.G. Larson and A. Massing, CutFEM: discretizing geometry and partial differential equations. Int. J. Numer. Meth. Eng. 104 (2015) 472–501. [Google Scholar]
- D. Cai, Z. Cai and S. Zhang, Robust equilibrated a posteriori error estimator for higher order finite element approximations to diffusion problems. Numer. Math. 144 (2020) 1–21. [Google Scholar]
- 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) 113673. [Google Scholar]
- D. Capatina and A. Gouasmi, Elliptic interface problem approximated by CutFEM: II. A posteriori error analysis based on equilibrated fluxes. Preprint arXiv: 2507.06740 (2025). [Google Scholar]
- D. Capatina, H. Derahaten and R. Luce, Equilibrated error estimators for CutFEM solutions of Poisson problem. Comput. Methods Appl. Mech. Eng. 410 (2023) 116035. [Google Scholar]
- S. Claus and P. Kerfriden, A cut finite element method for the Neumann problem on unfitted meshes with an artificial boundary conditions. Int. J. Numer. Meth. Eng. 113 (2018) 438–466. [Google Scholar]
- A. Demlow and B. Harrach, A posteriori error estimates for the finite element approximation of the inverse conductivity problem. SIAM J. Numer. Anal. 51 (2013) 2905–2931. [Google Scholar]
- A. Ern and M. Vohralík, A posteriori error estimation based on potential and flux reconstruction for the Heat equation. SIAM J. Numer. Anal. 48 (2010) 198–223. [CrossRef] [MathSciNet] [Google Scholar]
- A. Ern and M. Vohralík, Equilibrated flux a posteriori error estimates for high-order finite element approximations of diffusion problems. Numer. Math. 113 (2015) 198–223. [Google Scholar]
- A. Ern, I. Yotov and M. Vohralík, Conservative flux reconstruction for the discontinuous Galerkin method. SIAM J. Numer. Anal. 47 (2009) 198–223. [Google Scholar]
- A. Ern, A.F. Stephansen and P. Zunino, A discontinuous Galerkin method with weighted averages for advection-diffusion equations with locally small and anisotropic diffusivity. IMA J. Numer. Anal. 29 (2009) 235–256. [Google Scholar]
- S. Farina, S. Claus, J.S. Hale, A. Skupin and S.P. Bordas, A cut finite element method for spatially resolved energy metabolism models in complex neuro-cell morphologies with minimal remeshing. Adv. Model. Simul. Eng. Sci. 8 (2021) 1–32. [Google Scholar]
- A. Gouasmi, Numerical flux reconstruction for an interface problem and application to a posteriori error analysis. Ph.D. thesis, Université de Pau et des Pays de l'Adour (2024). [Google Scholar]
- R. Guo, Solving parabolic moving interface problems with dynamical immersed spaces on unfitted meshes: fully discrete analysis. SIAM J. Numer. Anal. 59 (2021) 797–828. [Google Scholar]
- P. Hansbo and M.G. Larson, An unfitted finite element method for elliptic interface problems. Comput. Methods Appl. Mech. Eng. 191 (2002) 5537–5552. [CrossRef] [Google Scholar]
- C. He, Z. Cai and S. Zhang, Robust equilibrated error estimators for discontinuous Galerkin methods for interface problems. SIAM J. Numer. Anal. 61 (2023) 2347–2373. [Google Scholar]
- J. Li, J.M. Melenk, B. Wohlmuth and J. Zou, A posteriori error estimate for fitted finite element methods for interface problems. Comput. Methods Appl. Mech. Eng. 199 (2010) 2347–2373. [Google Scholar]
- R. Luce and B. Wohlmuth, A local conservative flux for compatibility with transport in heterogeneous media. Comput. Methods Appl. Mech. Eng. 315 (2017) 799–830. [CrossRef] [Google Scholar]
- P.-A. Raviart and J.-M. Thomas, A mixed finite element method for second order elliptic problems, in Mathematical Aspects of the Finite Element Method. Lect. Notes in Math. Vol. 606. Springer-Verlag, Berlin (1977). [Google Scholar]
- R. Verfürth, A note on constant-free a posteriori error estimates. SIAM J. Numer. Anal. 47 (2009) 3180–3194. [Google Scholar]
- M. Vohralík, Guaranteed and fully robust a posteriori error estimates for conforming discretizations of diffusion problems with discontinuous coefficients. J. Sci. Comput. 46 (2011) 397–438. [Google Scholar]
- M. Vohralík and M.F. Wheeler, A posteriori error estimates, stopping criteria, and adaptivity for two-phase flows. Comput. Geosci. 17 (2013) 789–812. [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.