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All issues Volume 55 / No 5 (September-October 2021) ESAIM: M2AN, 55 5 (2021) 1873-1894 References
Open Access
Issue
ESAIM: M2AN
Volume 55, Number 5, September-October 2021
Page(s) 1873 - 1894
DOI https://doi.org/10.1051/m2an/2021042
Published online 17 September 2021
  1. C. Bacuta, J.H. Bramble and J.E. Pasciak, Shift Theorems for the Biharmonic Dirichlet Problem. In: T.F. Chan, Y. Huang, T. Tang, J. Xu, L.A. Ying (eds.) Recent Progress in Computational and Applied PDES. Springer, Boston, MA (2002) 1–26. [Google Scholar]
  2. M.S. Berger and P.C. Fife, Von Kármán equations and the buckling of a thin elastic plate, II plate with general edge conditions. Commun. Pure Appl. Math. 21 (1968) 227–241. [CrossRef] [Google Scholar]
  3. H. Blum and R. Rannacher, On mixed finite element methods in plate bending analysis. Comput. Mech. 6 (1990) 221–236. [Google Scholar]
  4. H. Blum, R. Rannacher and R. Leis, On the boundary value problem of the biharmonic operator on domains with angular corners. Math. Methods Appl. Sci. 2 (1980) 556–581. [Google Scholar]
  5. S.C. Brenner, M. Neilan, A. Reiser and L.-Y. Sung, A # interior penalty method for a von Kármán plate. Numerische Mathematik 135 (2017) 803–832. [Google Scholar]
  6. S.C. Brenner, L.-Y. Sung, H. Zhang and Y. Zhang, A quadratic # interior penalty method for the displacement obstacle problem of clamped Kirchhoff plates. SIAM J. Numer. Anal. 50 (2012) 3329–3350. [Google Scholar]
  7. S.C. Brenner, L.-Y. Sung, H. Zhang and Y. Zhang, A Morley finite element method for the displacement obstacle problem of clamped Kirchhoff plates. J. Comput. Appl. Math. 254 (2013) 31–42. [Google Scholar]
  8. S.C. Brenner, L.-Y. Sung and Y. Zhang, Finite element methods for the displacement obstacle problem of clamped plates. Math. Comput. 81 (2012) 1247–1262. [Google Scholar]
  9. F. Brezzi, Finite element approximations of the von Kármán equations. ESAIM: M2AN 12 (1978) 303–312. [Google Scholar]
  10. L.A. Caffarelli and A. Friedman, The obstacle problem for the biharmonic operator. Annali della Scuola Normale Superiore di Pisa-Classe di Scienze 6 (1979) 151–184. [Google Scholar]
  11. C. Carstensen, D. Gallistl and J. Hu, A discrete Helmholtz decomposition with Morley finite element functions and the optimality of adaptive finite element schemes. Comput. Math. Appl. 68 (2014) 2167–2181. [CrossRef] [Google Scholar]
  12. C. Carstensen, G. Mallik and N. Nataraj, A priori and a posteriori error control of discontinuous Galerkin finite element methods for the von Kármán equations. IMA J. Numer. Anal. 39 (2019) 167–200. [Google Scholar]
  13. C. Carstensen, G. Mallik and N. Nataraj, Nonconforming finite element discretization for semilinear problems with trilinear nonlinearity. IMA J. Numer. Anal. 41 (2021) 164–205. [Google Scholar]
  14. C. Carstensen and N. Nataraj, Adaptive Morley FEM for the von Kármán equations with optimal convergence rates. SIAM J. Numer. Anal. . Preprint: arXiv:1908.08013 (2020). [Google Scholar]
  15. C. Carstensen and S. Puttkammer, How to prove the discrete reliability for nonconforming finite element methods. J. Comput. Math. 38 (2020) 142–175. [Google Scholar]
  16. P.G. Ciarlet (ed.) The finite element method for elliptic problems, Vol. 4. Studies in Mathematics and its Applications. North-Holland Publishing Co., Amsterdam-New York-Oxford (1978). [Google Scholar]
  17. P.G. Ciarlet, Mathematical Elasticity: Volume II: Theory of Plates,Vol. 27. Studies in Mathematics and its Applications. Elsevier (1997). [Google Scholar]
  18. J. Frehse, Zum Differenzierbarkeitsproblem bei Variationsungleichungen höherer Ordnung. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 36 (1971) 140–149. [Google Scholar]
  19. D. Gallistl, Morley finite element method for the eigenvalues of the biharmonic operator. IMA J. Numer. Anal. 35 (2014) 1779–1811. [Google Scholar]
  20. R. Glowinski, Lectures on Numerical Methods for Non-linear Variational Problems. Springer-Verlag, Berlin-Heidelberg (2008). [Google Scholar]
  21. M. Hintermüller, K. Ito and K. Kunisch, The primal-dual active set strategy as a semismooth Newton method. SIAM J. Optim. 13 (2002) 865–888. [Google Scholar]
  22. D. Kinderlehrer and G. Stampacchia, An introduction to variational inequalities and their applications, Vol. 88. Pure and Applied Mathematics. Academic Press (1980). [Google Scholar]
  23. G.H. Knightly, An existence theorem for the von Kármán equations. Arch. Ration. Mech. Anal. 27 (1967) 233–242. [Google Scholar]
  24. G. Mallik and N. Nataraj, Conforming finite element methods for the von Kármán equations. Adv. Comput. Math. 42 (2016) 1031–1054. [Google Scholar]
  25. G. Mallik and N. Nataraj, A nonconforming finite element approximation for the von Kármán equations. ESAIM: M2AN 50 (2016) 433–454. [Google Scholar]
  26. E. Miersemann and H.D. Mittelmann, Stability in obstacle problems for the von Kármán plate. SIAM J. Math. Anal. 23 (1992) 1099–1116. [Google Scholar]
  27. T. Miyoshi, A mixed finite element method for the solution of the von Kármán equations. Numerische Mathematik 26 (1976) 255–269. [Google Scholar]
  28. A.D. Muradova and G.E. Stavroulakis, A unilateral contact model with buckling in von Kármán plates. Nonlinear Anal.: Real World Appl. 8 (2007) 1261–1271. [Google Scholar]
  29. K. Ohtake, J.T. Oden and N. Kikuchi, Analysis of certain unilateral problems in von Kármán plate theory by a penalty method-part 1. a variational principle with penalty. Comput. Methods Appl. Mech. Eng. 24 (1980) 187–213. [Google Scholar]
  30. K. Ohtake, J.T. Oden and N. Kikuchi, Analysis of certain unilateral problems in von Kármán plate theory by a penalty method-part 2. approximation and numerical analysis. Comput. Methods Appl. Mech. Eng. 24 (1980) 317–337. [Google Scholar]
  31. A. Quarteroni, Hybrid finite element methods for the von Kármán equations. Calcolo 16 (1979) 271–288. [CrossRef] [MathSciNet] [Google Scholar]
  32. L. Reinhart, On the numerical analysis of the von Kármán equations: mixed finite element approximation and continuation techniques. Numerische Mathematik 39 (1982) 371–404. [Google Scholar]
  33. S.-T. Yau and Y. Gao, Obstacle problem for von Kármán equations. Adv. Appl. Math. 13 (1992) 123–141. [Google Scholar]

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