Open Access
| Issue |
ESAIM: M2AN
Volume 59, Number 5, September-October 2025
|
|
|---|---|---|
| Page(s) | 2685 - 2715 | |
| DOI | https://doi.org/10.1051/m2an/2025062 | |
| Published online | 17 September 2025 | |
- M. Abbas, A. Ern and N. Pignet, Hybrid high-order methods for finite deformations of hyperelastic materials. Comput. Mech. 62 (2018) 909–928. [CrossRef] [MathSciNet] [Google Scholar]
- G. Allaire, Numerical Analysis and Optimization: An Introduction to Mathematical Modelling and Numerical Simulation. OUP Oxford (2007). [Google Scholar]
- P.F. Antonietti, F. Bonaldi and I. Mazzieri, A high-order discontinuous Galerkin approach to the elasto-acoustic problem. Comput. Methods Appl. Mech. Eng. 358 (2020) 112634. [Google Scholar]
- D. Appelo and N. Pettersson, A stable finite difference method for the elastic wave equation on complex geometries with free surfaces. CiCP 5 (2009) 84–107. [Google Scholar]
- E. Burman, A. Ern and M.A. Fernández, Explicit Runge–Kutta schemes and finite elements with symmetric stabilization for first-order linear pde systems. SIAM J. Numer. Anal. 48 (2010) 2019–2042. [CrossRef] [MathSciNet] [Google Scholar]
- E. Burman, O. Duran, A. Ern and M. Steins, Convergence analysis of hybrid high-order methods for the wave equation. J. Sci. Comput. 87 (2021) 91. [CrossRef] [Google Scholar]
- E. Burman, O. Duran and A. Ern, Hybrid high-order methods for the acoustic wave equation in the time domain. Comm. App. Math. Comp. Sci. 4 (2022) 597–633. [Google Scholar]
- E.T. Chung and B. Engquist, Optimal discontinuous Galerkin methods for wave propagation. SIAM J. Numer. Anal. 44 (2006) 2131–2158. [Google Scholar]
- M. Cicuttin, D. Di Pietro and A. Ern, Implementation of discontinuous skeletal methods on arbitrary-dimensional, polytopal meshes using generic programming. J. Comput. Appl. Math. 344 (2018) 852–874. [Google Scholar]
- M. Cicuttin, A. Ern and N. Pignet, Hybrid High-Order Methods. A Primer with Application to Solid Mechanics. SpringerBriefs in Mathematics. Springer, Cham (2021). [Google Scholar]
- B. Cockburn, J. Gopalakrishnan and R. Lazarov, Unified hybridization of discontinuous galerkin, mixed, and continuous Galerkin methods for second order elliptic problems. SIAM J. Numer. Anal. 47 (2009) 1319–1365. [CrossRef] [MathSciNet] [Google Scholar]
- B. Cockburn, D. Di Pietro and A. Ern, Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods. ESAIM: Math. Model. Numer. Anal. 50 (2016) 635–650. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
- G. Cohen, Higher-order numerical methods for transient wave equations. J. Acoust. Soc. 114 (2003) 21. [Google Scholar]
- D. Di Pietro, A. Ern and S. Lemaire, An arbitrary-order and compact-stencil discretization of diffusion on general meshes based on local reconstruction operators. J. Comput. Methods. Appl. Math. 14 (2014) 461–472. [Google Scholar]
- D. Di Pietro and A. Ern, A hybrid high-order locking-free method for linear elasticity on general meshes. Comput. Meth. Appl. Mech. Eng. 283 (2015) 1–21. [CrossRef] [Google Scholar]
- D.A. Di Pietro and J. Droniou, The Hybrid High-Order Method for Polytopal Meshes. Vol. 19 of Modeling, Simulation and Application. Springer, Cham (2020). [Google Scholar]
- S. Du and F.-J. Sayas, A note on devising HDG+ projections on polyhedral elements. Math. Comp. 90 (2021) 65–79. [Google Scholar]
- A. Ern and R. Khot, Explicit Runge–Kutta schemes with hybrid high-order methods for the wave equation in first order form. https://hal.science/hal-04763478/ (2024). [Google Scholar]
- A. Ern and M. Steins, Convergence analysis for the wave equation discretized with hybrid methods in space (HHO, HDG and WG) and the leapfrog scheme in time. J. Sci. Comput. 101 (2024) 28. [Google Scholar]
- R.S. Falk and G.R. Richter, Explicit finite element methods for symmetric hyperbolic equations. SIAM J. Numer. Anal. 36 (1999) 935–952. [Google Scholar]
- G.N. 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. SINUM 45 (2007) 2072–2097. [Google Scholar]
- M.J. Grote, A. Schneebeli and D. Schötzau, Discontinuous Galerkin finite element method for the wave equation. SIAM J. Numer. Anal. 44 (2006) 2408–2431. [Google Scholar]
- K.J. Marfurt, Accuracy of finite-difference and finite-element modelling of the scalar wave equation. Geophysics 49 (1984) 533–549. [Google Scholar]
- P. Monk and G. Richter, A discontinuous Galerkin method for linear symmetric hyperbolic systems in inhomogeneous media. J. Sci. Comput. 22 (2005) 443–477. [Google Scholar]
- N.A. Petersson and B. Sjögreen, High order accurate finite difference modeling of seismo-acoustic wave propagation in a moving atmosphere and a heterogeneous earth model coupled across a realistic topography. J. Sci. Comput. 74 (2017) 290–323. [Google Scholar]
- M. Steins, A. Ern, O. Jamond and F. Drui, Time-explicit hybrid high-order method for the nonlinear acoustic wave equation. ESAIM: Math. Model. Numer. Anal. 57 (2023) 2977–3006. [Google Scholar]
- C. Talischi, G. Paulino, A. Pereira and I. Menezes, Polymesher: a general-purpose mesh generator for polygonal elements written in matlab. Struct. Multidisc. Optim. 45 (2012) 309–328. [CrossRef] [Google Scholar]
- S. Terrana, J.P. Vilotte and L. Guillot, A spectral hybridizable discontinuous Galerkin method for elastic-acoustic wave propagation. Geophys. J. Int. 213 (2017) 574–602. [Google Scholar]
- R. van Vossen, J.O.A. Robertsson and C.H. Chapman, Finite-difference modeling of wave propagation in a fluid-solid configuration. Geophysics 67 (2002) 618–624. [Google Scholar]
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