Open Access
Issue
ESAIM: M2AN
Volume 58, Number 2, March-April 2024
Page(s) 695 - 721
DOI https://doi.org/10.1051/m2an/2024015
Published online 19 April 2024
  1. R.A. Adams and J.J.F. Fournier, Sobolev Spaces. Pure and Applied Mathematics (Amsterdam), 2nd edition. Vol. 140. Elsevier/Academic Press, Amsterdam (2003). [Google Scholar]
  2. A. Almqvist, C. Campañá, N. Prodanov and B.N.J. Persson, Interfacial separation between elastic solids with randomly rough surfaces: comparison between theory and numerical techniques. J. Mech. Phys. Solids 59 (2011) 2355–2369. [Google Scholar]
  3. S. Badia, F. Verdugo and A. Martín, The aggregated unfitted finite element method for elliptic problems. Comput. Methods Appl. Mech. Eng. 336 (2018) 533–553. [Google Scholar]
  4. R. Becker, E. Burman and P. Hansbo, A Nitsche extended finite element method for incompressible elasticity with discontinuous modulus of elasticity. Comput. Methods Appl. Mech. Eng. 198 (2009) 3352–3360. [Google Scholar]
  5. P.B. Bochev and M.D. Gunzburger, Finite element methods of least-squares type. SIAM Rev. 40 (1998) 789–837. [Google Scholar]
  6. S.P.A. Bordas, E. Burman, M.G. Larson and M.A. Olshanskii, editors, Geometrically Unfitted Finite Element Methods and Applications. Lecture Notes in Computational Science and Engineering, Vol. 121. Springer, Cham (2017), Held January 6–8, 2016. [Google Scholar]
  7. J.H. Bramble, R.D. Lazarov and J.E. Pasciak, A least-squares approach based on a discrete minus one inner product for first order systems. Math. Comput. 66 (1997) 935–955. [Google Scholar]
  8. J.H. Bramble, R.D. Lazarov and J.E. Pasciak, Least-squares methods for linear elasticity based on a discrete minus one inner product. Comput. Methods Appl. Mech. Eng. 191 (2001) 727–744. [Google Scholar]
  9. E. Burman, Ghost penalty. C. R. Math. Acad. Sci. Paris 348 (2010) 1217–1220. [CrossRef] [MathSciNet] [Google Scholar]
  10. E. Burman, S. Claus, P. Hansbo, M.G. Larson and A. Massing, CutFEM: discretizing geometry and partial differential equations. Int. J. Numer. Methods Eng. 104 (2015) 472–501. [Google Scholar]
  11. E. Burman, M. Cicuttin, G. Delay and A. Ern, An unfitted hybrid high-order method with cell agglomeration for elliptic interface problems. SIAM J. Sci. Comput. 43 (2021) A859–A882. [Google Scholar]
  12. Z. Cai and G. Moussa, First-order system least squares for the stress-displacement formulation: linear elasticity. SIAM J. Numer. Anal. 41 (2003) 715–730. [Google Scholar]
  13. Z. Cai and G. Moussa, Least-squares methods for linear elasticity. SIAM J. Numer. Anal. 42 (2004) 826–842. [Google Scholar]
  14. Z. Cai, T.A. Manteuffel, S.F. McCormick and S.V. Parter, First-order system least squares (FOSLS) for planar linear elasticity: pure traction problem. SIAM J. Numer. Anal. 35 (1998) 320–335. [Google Scholar]
  15. S. Chandrasekaran, M. Gu and T. Pals, A fast ULV decomposition solver for hierarchically semiseparable representations. SIAM J. Matrix Anal. Appl. 28 (2006) 603–622. [Google Scholar]
  16. Z. Chen and J. Moussa, Finite element methods and their convergence for elliptic and parabolic interface problems. Numer. Math. 79 (1998) 175–202. [Google Scholar]
  17. Z. Chen, K. Li and X. Xiang, An adaptive high-order unfitted finite element method for elliptic interface problems. Numer. Math. 149 (2021) 507–548. [Google Scholar]
  18. P. Ciarlet, Jr., Analysis of the Scott–Zhang interpolation in the fractional order Sobolev spaces. J. Numer. Math. 21 (2013) 173–180. [Google Scholar]
  19. L. Demkowicz and A. Moussa, H1, H(curl) and H(div)-conforming projection-based interpolation in three dimensions. Quasi-optimal p-interpolation estimates. Comput. Methods Appl. Mech. Eng. 194 (2005) 267–296. [Google Scholar]
  20. E. Di Nezza, G. Palatucci and E. Valdinoci, Hitchhiker’s guide to the fractional Sobolev spaces. Bull. Sci. Math. 136 (2012) 521–573. [Google Scholar]
  21. Z. Ding, A proof of the trace theorem of Sobolev spaces on Lipschitz domains. Proc. Amer. Math. Soc. 124 (1996) 591–600. [Google Scholar]
  22. T. Dupont and L.R. Scott, Polynomial approximation of functions in Sobolev spaces. Math. Comput. 34 (1980) 441–463. [Google Scholar]
  23. G. Dziuk and C.M. Elliott, Finite element methods for surface PDEs. Acta Numer. 22 (2013) 289–396. [Google Scholar]
  24. A. Ern and J.-L. Guermond, Evaluation of the condition number in linear systems arising in finite element approximations. ESAIM: M2AN 40 (2006) 29–48. [Google Scholar]
  25. H. Gao, Y. Huang and F. Abraham, Continuum and atomisitic studies of intersonic crack propagation. J. Mech. Phys. Solids 49 (2001) 2113–2132. [Google Scholar]
  26. L.V. Gibiansky and O. Sigmund, Multiphase composites with extremal bulk modulus. J. Mech. Phys. Solids 48 (2000) 461–498. [Google Scholar]
  27. P. Grisvard, Elliptic Problems in Nonsmooth Domains. Classics in Applied Mathematics. Vol. 69. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2011). [Google Scholar]
  28. R. Guo, T. Lin and Y. Lin, Error estimates for a partially penalized immersed finite element method for elasticity interface problems. ESAIM: M2AN 54 (2020) 1–24. [Google Scholar]
  29. R. Guo, Y. Lin and J. Zou, Solving two dimensional H(curl)-elliptic interface systems with optimal convergence on unfitted meshes. Preprint arXiv:2011.11905 (2020). [Google Scholar]
  30. C. Gürkan and A. Massing, A stabilized cut discontinuous Galerkin framework for elliptic boundary value and interface problems. Comput. Methods Appl. Mech. Eng. 348 (2019) 466–499. [Google Scholar]
  31. J. Guzmán and M. Olshanskii, Inf-sup stability of geometrically unfitted Stokes finite elements. Math. Comput. 87 (2018) 2091–2112. [Google Scholar]
  32. Y. Han, X.-P. Wang and X. Xie, An interface/boundary-unfitted extended HDG method for linear elasticity problems. J. Sci. Comput. 94 (2023) 61. [Google Scholar]
  33. A. Hansbo and P. Moussa, 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]
  34. A. Hansbo and P. Moussa, A finite element method for the simulation of strong and weak discontinuities in solid mechanics. Comput. Methods Appl. Mech. Eng. 193 (2004) 3523–3540. [Google Scholar]
  35. R. Hiptmair, J. Li and J. Zou, Convergence analysis of finite element methods for H(div; Ω)-elliptic interface problems. J. Numer. Math. 18 (2010) 187–218. [Google Scholar]
  36. 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. [Google Scholar]
  37. 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. [Google Scholar]
  38. D.Y. Kwak, S. Jin and D. Kyeong, A stabilized P1-nonconforming immersed finite element method for the interface elasticity problems. ESAIM: M2AN 51 (2017) 187–207. [Google Scholar]
  39. P.H. Leo, J.S. Lowengrub and Q. Nie, Microstructural evolution in orthotropic elastic media. J. Comput. Phys. 157 (2000) 44–88. [Google Scholar]
  40. Z. Li, The immersed interface method using a finite element formulation. Appl. Numer. Math. 27 (1998) 253–267. [Google Scholar]
  41. Z. Li and K. Moussa, The Immersed Interface Method: Numerical Solutions of PDEs Involving Interfaces and Irregular Domains. Frontiers in Applied Mathematics. Vol. 33. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2006). [Google Scholar]
  42. R. Li and F. Moussa, A least squares method for linear elasticity using a patch reconstructed space. Comput. Methods Appl. Mech. Eng. 363 (2020) 112902. [Google Scholar]
  43. R. Li, Q. Liu and F. Yang, A reconstructed discontinuous approximation on unfitted meshes to H(curl) and H(div) interface problems. Comput. Methods Appl. Mech. Eng. 403 (2023) 115723. [Google Scholar]
  44. L. Lin, J. Lu and L. Ying, Fast construction of hierarchical matrix representation from matrix-vector multiplication. J. Comput. Phys. 230 (2011) 4071–4087. [Google Scholar]
  45. T. Lin, D. Sheen and X. Zhang, A locking-free immersed finite element method for planar elasticity interface problems. J. Comput. Phys. 247 (2013) 228–247. [Google Scholar]
  46. T. Lin, D. Sheen and X. Zhang, A nonconforming immersed finite element method for elliptic interface problems. J. Sci. Comput. 79 (2019) 442–463. [Google Scholar]
  47. J.-L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications. Vol. I. Springer-Verlag, New York-Heidelberg (1972). Translated from the French by P. Kenneth, Die Grundlehren der mathematischen Wissenschaften, Band 181. MR 0350177. [Google Scholar]
  48. H. Liu, L. Zhang, X. Zhang and W. Zheng, Interface-penalty finite element methods for interface problems in H1, H(curl), and H(div). Comput. Methods Appl. Mech. Eng. 367 (2020) 113137. [Google Scholar]
  49. R. Massjung, An unfitted discontinuous Galerkin method applied to elliptic interface problems. SIAM J. Numer. Anal. 50 (2012) 3134–3162. [Google Scholar]
  50. F.-H. Rouet, X.S. Li, P. Ghysels and A. Napov, A distributed-memory package for dense hierarchically semi-separable matrix computations using randomization. ACM Trans. Math. Software 42 (2016) 35. [Google Scholar]
  51. L.R. Scott and S. Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math. Comput. 54 (1990) 483–493. [Google Scholar]
  52. G. Starke, A. Schwarz and J. Schröder, Analysis of a modified first-order system least squares method for linear elasticity with improved momentum balance. SIAM J. Numer. Anal. 49 (2011) 1006–1022. [Google Scholar]
  53. H. Wu and Y. Moussa, An unfitted hp-interface penalty finite element method for elliptic interface problems. J. Comput. Math. 37 (2019) 316–339. [Google Scholar]
  54. Y. Xi, J. Xia and R. Chan, A fast randomized eigensolver with structured LDL factorization update. SIAM J. Matrix Anal. Appl. 35 (2014) 974–996. [Google Scholar]
  55. J. Xia, S. Chandrasekaran, M. Gu and X.S. Li, Fast algorithms for hierarchically semiseparable matrices. Numer. Linear Algebra Appl. 17 (2010) 953–976. [Google Scholar]
  56. J. Xia, Z. Li and X. Ye, Effective matrix-free preconditioning for the augmented immersed interface method. J. Comput. Phys. 303 (2015) 295–312. [Google Scholar]
  57. F. Yang and X. Moussa, An unfitted finite element method by direct extension for elliptic problems on domains with curved boundaries and interfaces. J. Sci. Comput. 93 (2022) 75. [Google Scholar]
  58. X. Zhang, High order interface-penalty finite element methods for elasticity interface problems in 3D. Comput. Math. Appl. 114 (2022) 161–170. [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