Open Access
Issue
ESAIM: M2AN
Volume 58, Number 5, September-October 2024
Page(s) 1651 - 1680
DOI https://doi.org/10.1051/m2an/2024042
Published online 23 September 2024
  1. J. Badwaik and A.M. Ruf, Convergence rates of monotone schemes for conservation laws with discontinuous flux. SIAM J. Numer. Anal. 58 (2020) 607–629. [CrossRef] [MathSciNet] [Google Scholar]
  2. P. Batten, N. Clarke, C. Lambert and D.M. Causon, On the choice of wavespeeds for the HLLC Riemann solver. SIAM J. Sci. Comput. 18 (1997) 1553–1570. [CrossRef] [Google Scholar]
  3. M. Berger and A. Giuliani, A state redistribution algorithm for finite volume schemes on cut cell meshes. J. Comput. Phys. 428 (2021) 109820. [CrossRef] [Google Scholar]
  4. E. Burman, Ghost penalty. C. R. Math. 348 (2010) 1217–1220. [Google Scholar]
  5. E. Burman and P. Hansbo, Fictitious domain finite element methods using cut elements: II. A stabilized Nitsche method. Appl. Numer. Math. 62 (2012) 328–341. [Google Scholar]
  6. E. Burman, P. Hansbo and M.G. Larson, CutFEM based on extended finite element spaces. Numer. Math. 152 (2022) 331–369. [CrossRef] [MathSciNet] [Google Scholar]
  7. E. Burman, P. Hansbo and M.G. Larson, Explicit time stepping for the wave equation using cut fem with discrete extension. SIAM J. Sci. Comput. 44 (2022) A1254–A1289. [CrossRef] [Google Scholar]
  8. Z. Chen and Y. Liu, An arbitrarily high order unfitted finite element method for elliptic interface problems with automatic mesh generation. J. Comput. Phys. 491 (2023) 112384. [CrossRef] [Google Scholar]
  9. G. Chen, R. Pan and S. Zhu, Singularity formation for the compressible Euler equations. SIAM J. Math. Anal. 49 (2017) 2591–2614. [CrossRef] [MathSciNet] [Google Scholar]
  10. 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. [CrossRef] [MathSciNet] [Google Scholar]
  11. B. Cockburn and C.-W. Shu, TVB Runge–Kutta local projection discontinuous Galerkin finite element method for conservation laws. II. General framework. Math. Comput. 52 (1989) 411–435. [Google Scholar]
  12. B. Cockburn and C.-W. Shu, The Runge–Kutta discontinuous Galerkin method for conservation laws V: multidimensional systems. J. Comput. Phys. 141 (1998) 199–224. [Google Scholar]
  13. B. Cockburn, S.-Y. Lin and C.-W. Shu, TVB Runge–Kutta local projection discontinuous Galerkin finite element method for conservation laws III: one-dimensional systems. J. Comput. Phys. 84 (1989) 90–113. [Google Scholar]
  14. B. Cockburn, S. Hou and C.-W. Shu, The Runge–Kutta local projection discontinuous Galerkin finite element method for conservation laws. IV. The multidimensional case. Math. Comput. 54 (1990) 545–581. [Google Scholar]
  15. C.M. Dafermos and C.M. Dafermos, Hyperbolic Conservation Laws in Continuum Physics. Vol. 3. Springer (2005). [CrossRef] [Google Scholar]
  16. C. Engwer, S. May, A. Nüßing and F. Streitbürger, A stabilized DG cut cell method for discretizing the linear transport equation. SIAM J. Sci. Comput. 42 (2020) A3677–A3703. [CrossRef] [Google Scholar]
  17. T. Frachon and S. Zahedi, A cut finite element method for incompressible two-phase Navier–Stokes flows. J. Comput. Phys. 384 (2019) 77–98. [CrossRef] [MathSciNet] [Google Scholar]
  18. P. Fu and G. Kreiss, High order cut discontinuous Galerkin methods for hyperbolic conservation laws in one space dimension. SIAM J. Sci. Comput. 43 (2021) A2404–A2424. [CrossRef] [Google Scholar]
  19. P. Fu and Y. Xia, The positivity preserving property on the high order arbitrary Lagrangian–Eulerian discontinuous Galerkin method for Euler equations. J. Comput. Phys. 470 (2022) 111600. [CrossRef] [Google Scholar]
  20. P. Fu, T. Frachon, G. Kreiss and S. Zahedi, High order discontinuous cut finite element methods for linear hyperbolic conservation laws with an interface. J. Sci. Comput. 90 (2022) 1–39. [CrossRef] [Google Scholar]
  21. A. Giuliani, A two-dimensional stabilized discontinuous Galerkin method on curvilinear embedded boundary grids. SIAM J. Sci. Comput. 44 (2022) A389–A415. [CrossRef] [Google Scholar]
  22. J. Glimm, Solutions in the large for nonlinear hyperbolic systems of equations. Commun. Pure Appl. Math. 18 (1965) 697–715. [Google Scholar]
  23. S. Gottlieb, C.-W. Shu and E. Tadmor, Strong stability-preserving high-order time discretization methods. SIAM Rev. 43 (2001) 89–112. [Google Scholar]
  24. C. Gürkan, S. Sticko and A. Massing, Stabilized cut discontinuous Galerkin methods for advection-reaction problems. SIAM J. Sci. Comput. 42 (2020) A2620–A2654. [CrossRef] [Google Scholar]
  25. Y. Ha, C.L. Gardner, A. Gelb and C.-W. Shu, Numerical simulation of high Mach number astrophysical jets with radiative cooling. J. Sci. Comput. 24 (2005) 29–44. [CrossRef] [MathSciNet] [Google Scholar]
  26. P. Hansbo, M.G. Larson and S. Zahedi, A cut finite element method for a Stokes interface problem. Appl. Numer. Math. 85 (2014) 90–114. [CrossRef] [MathSciNet] [Google Scholar]
  27. J.S. Hesthaven, Numerical Methods for Conservation Laws. Society for Industrial and Applied Mathematics, Philadelphia, PA (2018). [CrossRef] [Google Scholar]
  28. J.S. Hesthaven and T. Warburton, Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications. Springer Science & Business Media (2007). [Google Scholar]
  29. 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. [CrossRef] [Google Scholar]
  30. 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. [CrossRef] [MathSciNet] [Google Scholar]
  31. V.P. Korobeinikov, Problems of Point Blast Theory. Springer Science & Business Media (1991). [Google Scholar]
  32. F. Kummer, Extended discontinuous Galerkin methods for two-phase flows: the spatial discretization. Int. J. Numer. Methods Eng. 109 (2017) 259–289. [CrossRef] [Google Scholar]
  33. M.G. Larson and S. Zahedi, Conservative cut finite element methods using macroelements. Comput. Methods Appl. Mech. Eng. 414 (2023) 116141. [CrossRef] [Google Scholar]
  34. T. Linde, P. Roe, T. Linde and P. Roe, Robust Euler codes, in 13th Computational Fluid Dynamics Conference. (1997) 2098. [Google Scholar]
  35. R. Massjung, An unfitted discontinuous Galerkin method applied to elliptic interface problems. SIAM J. Numer. Anal. 50 (2012) 3134–3162. [Google Scholar]
  36. A. Massing, M.G. Larson, A. Logg and M.E. Rognes, A stabilized Nitsche fictitious domain method for the Stokes problem. J. Sci. Comput. 61 (2014) 604–628. [Google Scholar]
  37. S. May and F. Streitbürger, DoD stabilization for non-linear hyperbolic conservation laws on cut cell meshes in one dimension. Appl. Math. Comput. 419 (2022) 126854. [Google Scholar]
  38. J. Modisette and D. Darmofal, Toward a robust, higher-order cut-cell method for viscous flows, in 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition (2010) 721. [Google Scholar]
  39. B. Müller, S. Kr¨amer-Eis, F. Kummer and M. Oberlack, A high-order discontinuous Galerkin method for compressible flows with immersed boundaries. Int. J. Numer. Methods Eng. 110 (2017) 3–30. [CrossRef] [Google Scholar]
  40. R. Qin and L. Krivodonova, A discontinuous Galerkin method for solutions of the Euler equations on Cartesian grids with embedded geometries. J. Comput. Sci. 4 (2013) 24–35. [CrossRef] [Google Scholar]
  41. J. Qiu and C.-W. Shu, Runge–Kutta discontinuous Galerkin method using WENO limiters. SIAM J. Sci. Comput. 26 (2005) 907–929. [CrossRef] [MathSciNet] [Google Scholar]
  42. S. Schoeder, S. Sticko, G. Kreiss and M. Kronbichler, High-order cut discontinuous Galerkin methods with local time stepping for acoustics. Int. J. Numer. Methods Eng. 121 (2020) 2979–3003. [CrossRef] [Google Scholar]
  43. L.I. Sedov, Similarity and Dimensional Methods in Mechanics. CRC Press (1993). [Google Scholar]
  44. C.-W. Shu, Discontinuous Galerkin methods: general approach and stability. Numer. Sol. Part. Differ. Equ. 201 (2009) 149–201. [Google Scholar]
  45. E.M. Stein, Singular Integrals and Differentiability Properties of Functions (PMS-30). Vol. 30. Princeton University Press (2016). [Google Scholar]
  46. S. Sticko and G. Kreiss, A stabilized Nitsche cut element method for the wave equation. Comput. Methods Appl. Mech. Eng. 309 (2016) 364–387. [CrossRef] [Google Scholar]
  47. S. Sticko and G. Kreiss, Higher order cut finite elements for the wave equation. J. Sci. Comput. 80 (2019) 1867–1887. [CrossRef] [MathSciNet] [Google Scholar]
  48. S. Tan and C.-W. Shu, Inverse Lax-Wendroff procedure for numerical boundary conditions of conservation laws. J. Comput. Phys. 229 (2010) 8144–8166. [Google Scholar]
  49. E. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction. Springer Science & Business Media (2009). [CrossRef] [Google Scholar]
  50. P. Woodward and P. Colella, The numerical simulation of two-dimensional fluid flow with strong shocks. J. Comput. Phys. 54 (1984) 115–173. [Google Scholar]
  51. L. Yang, S. Li, Y. Jiang, C.-W. Shu, M. Zhang and Z.-C. Shi, Inverse Lax-Wendroff boundary treatment of discontinuous Galerkin method for 1D conservation laws. Commun. Appl. Math. Comput. (2024) 1–31. [Google Scholar]
  52. X. Zhang and C.-W. Shu, On maximum-principle-satisfying high order schemes for scalar conservation laws. J. Comput. Phys. 229 (2010) 3091–3120. [CrossRef] [MathSciNet] [Google Scholar]
  53. X. Zhang and C.-W. Shu, On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes. J. Comput. Phys. 229 (2010) 8918–8934. [CrossRef] [MathSciNet] [Google Scholar]

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