EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 57 / No 1 (January-February 2023) ESAIM: M2AN, 57 1 (2023) 107-141 References
Open Access
Issue
ESAIM: M2AN
Volume 57, Number 1, January-February 2023
Page(s) 107 - 141
DOI https://doi.org/10.1051/m2an/2022026
Published online 12 January 2023
  1. C. Bacuta, J.H. Bramble and J. Xu, Regularity estimates for elliptic boundary value problems in Besov spaces. Math. Comp. 72 (2003) 1577–1595 (electronic) [Google Scholar]
  2. M. Bernkopf and J.M. Melenk, Analysis of the hp-version of a first order system least squares method for the Helmholtz equation, in Advanced Finite Element Methods with Applications: Selected Papers from the 30th Chemnitz Finite Element Symposium 2017, edited by T. Apel, U. Langer, A. Meyer and O. Steinbach. Springer International Publishing, Cham (2019) 57–84. [CrossRef] [Google Scholar]
  3. M. Bernkopf and J.M. Melenk, Optimal convergence rates in L2 for a first order system least squares finite element method. Part I: homogeneous boundary conditions. Preprint https://arxiv.org/abs/2012.12919 (2020). [Google Scholar]
  4. P. Bochev and M. Gunzburger, On least-squares finite element methods for the Poisson equation and their connection to the Dirichlet and Kelvin principles. SIAM J. Numer. Anal. 43 (2005) 340–362. [CrossRef] [MathSciNet] [Google Scholar]
  5. P.B. Bochev and M.D. Gunzburger, Least-Squares Finite Element Methods. Vol. 166 of Applied Mathematical Sciences. Springer, New York (2009). [Google Scholar]
  6. D. Boffi, F. Brezzi and M. Fortin, Mixed Finite Element Methods and Applications. Vol. 44 of Springer Series in Computational Mathematics. Springer, Heidelberg (2013). [Google Scholar]
  7. Z. Cai, R. Lazarov, T.A. Manteuffel and S.F. McCormick, First-order system least squares for second-order partial differential equations. I. SIAM J. Numer. Anal. 31 (1994) 1785–1799. [Google Scholar]
  8. Z. Cai, T.A. Manteuffel and S.F. McCormick, First-order system least squares for the Stokes equations, with application to linear elasticity. SIAM J. Numer. Anal. 34 (1997) 1727–1741. [CrossRef] [MathSciNet] [Google Scholar]
  9. Z. Cai, T.A. Manteuffel and S.F. McCormick, First-order system least squares for second-order partial differential equations. II. SIAM J. Numer. Anal. 34 (1997) 425–454. [CrossRef] [MathSciNet] [Google Scholar]
  10. H. Chen and W. Qiu, A first order system least squares method for the Helmholtz equation. J. Comput. Appl. Math. 309 (2017) 145–162. [CrossRef] [MathSciNet] [Google Scholar]
  11. L. Demkowicz and I. Babuška, p interpolation error estimates for edge finite elements of variable order in two dimensions. SIAM J. Numer. Anal. 41 (2003) 1195–1208. [CrossRef] [MathSciNet] [Google Scholar]
  12. A. Ern, T. Gudi, I. Smears and M. Vohralk, Equivalence of local- and global-best approximations, a simple stable local commuting projector, and optimal hp approximation estimates in H(div). IMA J. Numer. Anal. 42 (2022) 1023–1049. [CrossRef] [MathSciNet] [Google Scholar]
  13. L.C. Evans, Partial Differential Equations, Vol. 19 of Graduate Studies in Mathematics, 2nd edition. American Mathematical Society, Providence, RI (2010). [CrossRef] [Google Scholar]
  14. P. Grisvard, Elliptic Problems in Nonsmooth Domains. Vol. 69 of Classics in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2011). Reprint of the 1985 original [MR0775683], With a foreword by Susanne C, Brenner [Google Scholar]
  15. D.C. Jespersen, A least squares decomposition method for solving elliptic equations. Math. Comp. 31 (1977) 873–880. [CrossRef] [MathSciNet] [Google Scholar]
  16. W. McLean, Strongly Elliptic Systems and Boundary Integral Equations. Cambridge University Press, Cambridge (2000). [Google Scholar]
  17. J.M. Melenk and C. Rojik, On commuting p-version projection-based interpolation on tetrahedra. Math. Comp. 89 (2020) 45–87. [Google Scholar]
  18. J.M. Melenk and S.A. Sauter, Wavenumber-explicit hp-FEM analysis for Maxwell’s equations with transparent boundary conditions. Found. Comput. Math. 21 (2021) 125–241. [CrossRef] [MathSciNet] [Google Scholar]
  19. P. Monk, Finite Element Methods for Maxwell’s Equations. Numerical Mathematics and Scientific Computation. Oxford University Press, New York (2003). [Google Scholar]
  20. C. Rojik, p-version projection based interpolation. Ph.D. thesis, TU Wien (2019). https://repositum.tuwien.at/handle/20.500.12708/17. [Google Scholar]
  21. G. Savaré, Regularity results for elliptic equations in Lipschitz domains. J. Funct. Anal. 152 (1998) 176–201. [CrossRef] [MathSciNet] [Google Scholar]
  22. J. Schöberl, Finite Element Software NETGEN/NGSolve version 6.2. https://ngsolve.org/ [Google Scholar]
  23. J. Schöberl, NETGEN – An advancing front 2D/3D-mesh generator based on abstract rules. Comput. Visual. Sci. 1 (1997) 41–52. [CrossRef] [Google Scholar]
  24. L. Tartar, An Introduction to Sobolev Spaces and Interpolation Spaces. Vol. 3 of Lecture Notes of the Unione Matematica Italiana. Springer, Berlin; UMI, Bologna (2007). [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