Open Access
Issue
ESAIM: M2AN
Volume 57, Number 5, September-October 2023
Page(s) 2681 - 2699
DOI https://doi.org/10.1051/m2an/2022071
Published online 14 September 2023
  1. L. Alzaben, F. Bertrand and D. Boffi, Computation of eigenvalues in linear elasticity with least-squares finite elements: dealing with the mixed system, in WCCM-ECCOMAS2020. SCIPEDIA (2021). [Google Scholar]
  2. F. Bertrand and D. Boffi, First order least-squares formulations for eigenvalue problems. IMA J. Numer. Anal. 42 (2022) 1339–1363. [CrossRef] [MathSciNet] [Google Scholar]
  3. F. Bertrand and D. Boffi, Least-squares formulations for eigenvalue problems associated with linear elasticity. Comput. Math. App. 95 (2021) 19–27. [Google Scholar]
  4. F. Bertrand, D. Boffi and H. Schneider, Discontinuous Petrov-Galerkin approximation of eigenvalue problems. Comput. Methods Appl. Math. (2022). DOI: 10.1515/cmam-2022-0069. [Google Scholar]
  5. F. Bertrand and H. Schneider, Least-squares methods for linear elasticity: refined error estimates, inWCCM-ECCOMAS2020. SCIPEDIA (2021). [Google Scholar]
  6. T. Bouma, J. Gopalakrishnan and A. Harb, Convergence rates of the DPG method with reduced test space degree. Comput. Math. Appl. 68 (2014) 1550–1561. [CrossRef] [MathSciNet] [Google Scholar]
  7. J. Bramwell, L. Demkowicz, J. Gopalakrishnan and W. Qiu, A locking-free ℎp DPG method for linear elasticity with symmetric stresses. Numer. Math. 122 (2012) 671–707. [CrossRef] [MathSciNet] [Google Scholar]
  8. C. Carstensen, M. Eigel and J. Gedicke, Computational competition of symmetric mixed FEM in linear elasticity. Comput. Methods Appl. Mech. Eng. 200 (2011) 2903–2915. [CrossRef] [Google Scholar]
  9. C. Carstensen, L. Demkowicz and J. Gopalakrishnan, A posteriori error control for DPG methods. SIAM J. Numer. Anal. 52 (2014) 1335–1353. [MathSciNet] [Google Scholar]
  10. C. Carstensen, L. Demkowicz and J. Gopalakrishnan, Breaking spaces and forms for the DPG method and applications including Maxwell equations. Comput. Math. Appl. 72 (2016) 494–522. [CrossRef] [MathSciNet] [Google Scholar]
  11. C. Carstensen and F. Hellwig, Low-order discontinuous Petrov-Galerkin finite element methods for linear elasticity. SIAM J. Numer. Anal. 54 (2016) 3388–3410. [CrossRef] [MathSciNet] [Google Scholar]
  12. L. Demkowicz and J. Gopalakrishnan, A class of discontinuous Petrov-Galerkin methods. Part I: the transport equation. Comput. Methods Appl. Mech. Eng. 199 (2010) 1558–1572. [CrossRef] [Google Scholar]
  13. L. Demkowicz and J. Gopalakrishnan, A class of discontinuous Petrov-Galerkin methods. II. Optimal test functions. Numer. Methods Part. Differ. Equ. 27 (2011) 70–105. [CrossRef] [Google Scholar]
  14. L. Demkowicz, J. Gopalakrishnan and A.H. Niemi, A class of discontinuous Petrov-Galerkin methods. Part III: adaptivity. Appl. Numer. Math. 62 (2012) 396–427. [CrossRef] [MathSciNet] [Google Scholar]
  15. A. Ern and J.-L. Guermond, Finite Elements I – Approximation and Interpolation. Vol. 72 of Texts in Applied Mathematics, Springer, Cham (2021). [CrossRef] [Google Scholar]
  16. T. Führer, Superconvergence in a DPG method for an ultra-weak formulation. Comput. Math. Appl. 75 (2018) 1705–1718. [CrossRef] [MathSciNet] [Google Scholar]
  17. T. Führer, Superconvergent dpg methods for second-order elliptic problems. Comput. Methods Appl. Math. 19 (2019) 483–502. [CrossRef] [MathSciNet] [Google Scholar]
  18. G. Gatica, A. Márquez and S. Meddahi, Analysis of the coupling of primal and dual-mixed finite element methods for a two-dimensional fluid-solid interaction problem. SIAM J. Numer. Anal. 45 (2007) 2072–2097. [CrossRef] [MathSciNet] [Google Scholar]
  19. G. Gatica, A. Márquez and S. Meddahi, Analysis of the coupling of lagrange and arnold-falk-winther finite elements for a fluid-solid interaction problem in three dimensions. SIAM J. Numer. Anal. 50 (2012) 1648–1674. [CrossRef] [MathSciNet] [Google Scholar]
  20. J. Gopalakrishnan and J. Guzmán, Symmetric nonconforming mixed finite elements for linear elasticity. SIAM J. Numer. Anal. 49 (2011) 1504–1520. [CrossRef] [MathSciNet] [Google Scholar]
  21. J. Gopalakrishnan and W. Qiu, An analysis of the practical DPG method. Math. Comp. 83 (2014) 537–552. [Google Scholar]
  22. P. Grisvard, Elliptic Problems in Nonsmooth Domains. Vol. 24 of Monographs and Studies in Mathematics. Pitman (Advanced Publishing Program), Boston, MA (1985). [Google Scholar]
  23. B. Keith, F. Fuentes and L. Demkowicz, The DPG methodology applied to different variational formulations of linear elasticity. Comput. Methods Appl. Mech. Eng. 309 (2016) 579–609. [CrossRef] [Google Scholar]
  24. P.-A. Raviart and J.M. Thomas, A mixed finite element method for 2nd order elliptic problems, in Mathematical Aspects of Finite Element Methods (Proc. Conf., Consiglio Naz. delle Ricerche (C.N.R.), Rome, 1975). Lecture Notes in Math. Vol. 606. Springer, Berlin (1977) 292–315. [Google Scholar]
  25. L.R. Scott and S. Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math. Comp. 54 (1990) 483–493. [Google Scholar]
  26. R. Stenberg, A family of mixed finite elements for the elasticity problem. Numer. Math. 53 (1988) 513–538. [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