EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 55 / No 4 (July-August 2021) ESAIM: M2AN, 55 4 (2021) 1507-1543 References
Open Access
Issue
ESAIM: M2AN
Volume 55, Number 4, July-August 2021
Page(s) 1507 - 1543
DOI https://doi.org/10.1051/m2an/2021030
Published online 29 July 2021
  1. J. Albella, H. Ben Dhia, S. Imperiale and J. Rodrguez, Mathematical and numerical study of transient wave scattering by obstacles with a new class of Arlequin coupling. SIAM J. Numer. Anal. 57 (2019) 2436–2468. [CrossRef] [Google Scholar]
  2. E. Bécache and P. Joly, Space-time mesh refinement for elastodynamics. Comput. Methods Appl. Mech. Eng. 194 (2005) 355–366. [CrossRef] [Google Scholar]
  3. E. Bécache, J. Rodrguez and C. Tsogka, Convergence results of the fictitious domain method for a mixed formulation of the wave equation with a Neumann boundary condition. ESAIM: M2AN 43 (2009) 377–398. [CrossRef] [EDP Sciences] [Google Scholar]
  4. F. Ben Belgacem, C. Bernardi, N. Chorfi and Y. Maday, Inf-sup conditions for the mortar spectral element discretization of the Stokes problem. Numer. Math. 85 (2000) 257–281. [CrossRef] [MathSciNet] [Google Scholar]
  5. D. Boffi, F. Brezzi and M. Fortin, Mixed Finite Element Methods and Applications. Springer Science (2013). [CrossRef] [Google Scholar]
  6. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer Science (2012) 15. [Google Scholar]
  7. J. Chabassier and S. Imperiale, Fourth order energy-preserving locally implicit time discretisation for linear wave equations. Int. J. Numer. Methods Eng. 106 (2016) 593–622. [CrossRef] [Google Scholar]
  8. J. Chabassier and S. Imperiale, Space/Time convergence analysis of a class of conservative schemes for linear wave equations. C.R. Math. 355 (2017) 282–289. [CrossRef] [Google Scholar]
  9. J. Chabassier, J. Diaz and S. Imperiale, Construction and analysis of fourth order, energy consistent, family of explicit time discretizations for dissipative linear wave equations. ESAIM: M2AN 54 (2020) 845–878. [CrossRef] [EDP Sciences] [Google Scholar]
  10. G. Cohen, Higher-order Numerical Methods for Transient Wave Equations. Springer-Verlag (2001). [Google Scholar]
  11. G. Cohen, P. Joly and N. Tordjman, Higher-order finite elements with mass-lumping for the 1D wave equation. Finite Elem. Anal. Des. 16 (1994) 329–336. [CrossRef] [Google Scholar]
  12. G. Cohen, P. Joly, J.E. Roberts and N. Tordjman, Higher-order triangular finite elements with mass lumping for the wave equation. SIAM: J. Numer. Anal. 38 (2001) 2047–2078. [CrossRef] [Google Scholar]
  13. F. Collino, T. Fouquet and P. Joly, A conservative space-time mesh refinement method for the 1-d wave equation. Part I: Construction. Part I: Construction. Numer. Math. 95 (2003) 197–221. [CrossRef] [Google Scholar]
  14. F. Collino, T. Fouquet and P. Joly, A conservative space-time mesh refinement method for the 1-D wave equation. II. Analysis. Numer. Math. 95 (2003) 223–251. [CrossRef] [MathSciNet] [Google Scholar]
  15. C. Constantin, M. Hochbruck and A. Sturm, On leapfrog-Chebyshev schemes. SIAM J. Numer. Anal. 58 (2020) 2404–2433. [CrossRef] [Google Scholar]
  16. R. Dautray, J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology – Volume 5 and 6 – Evolution Problems I and II. Springer-Verlag Berlin (2000). [Google Scholar]
  17. G. Derveaux, P. Joly and J. Rodrguez, Effective Computational Methods for Wave Propagation. Chap 13: Space Time Mesh Refinement Methods. Chapman and Hall/CRC (2008). [Google Scholar]
  18. S. Descombes, S. Lanteri and L. Moya, Locally implicit time integration strategies in a discontinuous Galerkin method for Maxwell’s equations. J. Sci. Comput. 56 (2013) 190–218. [CrossRef] [Google Scholar]
  19. J. Diaz and M.J. Grote, Energy conserving explicit local time-stepping for second-order wave equations. SIAM J. Sci. Comput. 31 (2009) 1985–2014. [CrossRef] [Google Scholar]
  20. J. Diaz and M.J. Grote, Multi-level explicit local time-stepping methods for second-order wave equations. Comput. Methods Appl. Mech. Eng. 291 (2015) 240–265. [Google Scholar]
  21. V. Dolean, H. Fahs, L. Fezoui and S. Lanteri, Locally implicit discontinuous Galerkin method for time domain electromagnetics. J. Comput. Phys. 229 (2010) 512–526. [CrossRef] [MathSciNet] [Google Scholar]
  22. M. Dumbser, M. Käser and E.F. Toro, An arbitrary high-order Discontinuous Galerkin method for elastic waves on unstructured meshes – V. Local time stepping and p-adaptivity. Geophys. J. Int. 171 (2007) 695–717. [CrossRef] [Google Scholar]
  23. M. Durufle, P. Grob and P. Joly, Influence of Gauss and Gauss-Lobatto quadrature rules on the accuracy of a quadrilateral finite element method in the time domain. Numer. Methods Part. Differ. Equ. 25 (2009) 526–551. [CrossRef] [Google Scholar]
  24. J.C. Gilbert and P. Joly, Higher order time stepping for second order hyperbolic problems and optimal CFL conditions. Part. Differ. Equ. 16 (2008) 67–93. [Google Scholar]
  25. M.J. Grote and T. Mitkova, Explicit local time-stepping methods for Maxwell’s equations. J. Comput. Appl. Math. 234 (2010) 3283–3302. [CrossRef] [MathSciNet] [Google Scholar]
  26. M.J. Grote, M. Mehlin and S. Sauter, Convergence analysis of energy conserving explicit local time-stepping methods for the wave equation. SIAM J. Numer. Anal. 56 (2018) 994–1021. [CrossRef] [Google Scholar]
  27. M.J. Grote, S. Michel and S. Sauter, Stabilized leapfrog based local time-stepping method for the wave equation. Preprint: arXiv:2005.13350 (2021). [Google Scholar]
  28. P. Hauret and P. Le Tallec, A discontinuous stabilized mortar method for general 3D elastic problems. Comput. Methods Appl. Mech. Eng. 196 (2007) 4881–4900. [Google Scholar]
  29. J.S. Hesthaven and T. Warburton, Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications. Springer Science & Business Media (2007). [Google Scholar]
  30. M. Hochbruck and A. Sturm, Error analysis of a second-order locally implicit method for linear Maxwell’s equations. SIAM J. Numer. Anal. 54 (2016) 3167–3191. [CrossRef] [Google Scholar]
  31. M. Hochbruck and A. Sturm, Upwind discontinuous Galerkin space discretisation and locally implicit time integration for linear Maxwell’s equations. Math. Comput. 88 (2019) 1121–1153. [CrossRef] [Google Scholar]
  32. W. Hundsdorfer and J.G. Verwer, Numerical solution to Time-Dependent Advection-Diffusion-Reaction Equations, Springer Series in Computational Mathematics (2003). [CrossRef] [Google Scholar]
  33. P. Joly and J. Rodrguez, An error analysis of conservative space-time mesh refinement methods for the one-dimensional wave equation. SIAM J. Numer. Anal. 43 (2005) 825–859. [CrossRef] [Google Scholar]
  34. P. Joly and J. Rodrguez, Optimized higher order time discretisation of second order hyperbolic problems: construction and numerical study. J. Comput. Appl. Math. 234 (2010) 1953–1961. [CrossRef] [Google Scholar]
  35. Y. Maday and A.T. Patera, Spectral element methods for the incompressible Navier-Stokes equations. In: State-of-the-art Surveys On Computational Mechanics. American Society of Mechanical Engineers (1989). [Google Scholar]
  36. Y. Maday, C. Mavriplis and A.T. Patera, Nonconforming mortar element methods: application to spectral discretisations. In: Domain Decomposition Methods. SIAM Philadelphia (1989) 392–418. [Google Scholar]
  37. J. Rodrguez, Une nouvelle méthode de raffinement de maillage spatio-temporel pour l’équation des ondes. C. R. Math. Acad. Sci. Paris 339 (2004) 445–450. [CrossRef] [Google Scholar]
  38. J. Rodrguez, A spurious-free space-time mesh refinement for elastodynamics. Int. J. Multiscale Comput. Eng. 6 (2008) 263–279. [CrossRef] [Google Scholar]
  39. T. Rylander, Stability of Explicit-Implicit Hybrid Time-Stepping Schemes for Maxwell’s Equations. J. Comput. Phys. 179 (2002) 426–438. [CrossRef] [Google Scholar]
  40. P.J. van Der Houwen, B.P. Sommeijer, On the internal stability of explicit, m-Stage Runge-Kutta methods for large m-Values. J. Appl. Math. Mech. 60 (1980) 479–485. [Google Scholar]
  41. B.I. Wohlmuth, A mortar finite element method using dual spaces for the lagrange multiplier. SIAM J. Numer. Anal. 38 (2000) 989–1012. [Google Scholar]
  42. B.I. Wohlmuth, Discretization Methods and Iterative Solvers Based on Domain Decomposition. In Vol. 17 of Lecture Notes in Computational Science and Engineering. Springer, USA (2001). [CrossRef] [Google Scholar]
  43. https://eigen.tuxfamily.org/. [Google Scholar]
  44. https://gitlab.inria.fr/local-schemes/supplementary-sources. [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