High order immersed hybridized difference methods for elliptic interface problems

References

[1] Adjerid, S., Babuška, I., Guo, R., and Lin, T. An enriched immersed finite element method for interface problems with nonhomogeneous jump conditions. Computer Methods in Applied Mechanics and Engineering 404 (2023), 1–37.10.1016/j.cma.2022.115770Search in Google Scholar

[2] Chessa, J., Smolinski, P., and Belytschko, T. The extended finite element method(xfem) for solidification problems. Internat. J. Numer. Methods Engrg. 53 (2002), 1959–1977.10.1002/nme.386Search in Google Scholar

[3] Feng, Q., Han, B., and Minev, P. Sixth order compact finite difference schemes for poisson interface problems with singular sources. Comp. Math. Appl. 99 (2021), 2–25.10.1016/j.camwa.2021.07.020Search in Google Scholar

[4] Feng, Q., Han, B., and Minev, P. A high order compact finite difference scheme for elliptic interface problems with discontinuous and high-contrast coefficients. Appl. Math. Comp. 431 (2022), 1–24.10.1016/j.amc.2022.127314Search in Google Scholar

[5] Guo, R., and Lin, T. A higher degree immersed finite element method based on a cauchy extension for elliptic interface problems. SINUM 57 (2019), 1545–1573.10.1137/18M121318XSearch in Google Scholar

[6] He, X.-M., Lin, T., and Lin, Y. A bilinear immersed finite volume element method for the diffusion equation with discontinuous coefficient. Comm. in Comp. Phys. 6, 1 (2009), 185–202.10.4208/cicp.2009.v6.p185Search in Google Scholar

[7] Huang, H., And Li, Z. Convergence analysis of the immersed interface method. IMA J. Numer. Anal. 19, 4 (1999), 583–608.Search in Google Scholar

[8] Huang, H., and Li, Z. Convergence analysis of the immersed interface method. IMAJ.Numer.Anal. 19 (1999), 583–608.10.1093/imanum/19.4.583Search in Google Scholar

[9] Jeon, Y. Hybrid difference methods for pdes. J. Sci. Comput. 64 (2015), 508–521.10.1007/s10915-014-9941-ySearch in Google Scholar

[10] Jeon, Y. An immersed hybrid difference method for the elliptic interface equation. Japan J. of Indus. and App. Math. 39 (2022), 669–692.10.1007/s13160-022-00503-4Search in Google Scholar

[11] Jeon, Y., Park, E.-J., and Shin, D.-W. Hybrid spectral difference methods for an elliptic equation. Comput. Meth. Appl. Math. 17 (2017), 253–267.10.1515/cmam-2016-0043Search in Google Scholar

[12] Jeon, Y., and Sheen, D. Upwind hybrid spectral difference methods for the steady–state navier–stokes equations. In Contemporary Computational Mathematics–A Celebration of the 80th Birthday of Ian Sloan (2018), J. Dick and F. Kuo, Eds., Springer-Verlag, pp. 632–641.10.1007/978-3-319-72456-0_28Search in Google Scholar

[13] Jeon, Y., and Yi, S.-Y. The immersed interface hybridized difference method for parabolic interface problems. Numer. Math. Theor. Meth. Appl. 15 (2022), 336–359.10.4208/nmtma.OA-2021-0154Search in Google Scholar

[14] Lai, M. C., and Peskin, C. S. An immersed boundary method with formal second-order accuracy and reduced numerical viscosity. J. Comput. Phys. 160 (2000), 705–719.10.1006/jcph.2000.6483Search in Google Scholar

[15] Leveque, R. J., and Li, Z. The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM J. Numer. Anal. 31, 4 (1994), 1019–1044.10.1137/0731054Search in Google Scholar

[16] Leveque, R. J., and Li, Z. Immersed interface methods for stokes flow with elastic boundaries or surface tension. SIAM J. Sci. Comput. 18, 3 (1997), 709–735.10.1137/S1064827595282532Search in Google Scholar

[17] Li, Z., and Ito, K. The immersed interface method: Numerical solutions of PDEs involving interfaces and irregular domains, Frontiers in Applied Mathematics. SIAM Pub., 2006.10.1137/1.9780898717464Search in Google Scholar

[18] Li, Z., Lin, T., Lin, Y., and Rogers, R. C. An immersed finite element space and its approximation capability. Numer. Meth. PDEs 20, 3 (2004), 338–367.10.1002/num.10092Search in Google Scholar

[19] Marques, A., Nave, J.-C., and Rosales, R. R. A correction function method for poisson problems with interface jump conditions. J. Comp. Phys. 230 (2011), 7567–7597.10.1016/j.jcp.2011.06.014Search in Google Scholar

[20] Marques, A. N., Nave, J.-C., and Rosales, R. R. High order solution of poisson problems with piecewise constant coefficients and interface jumps. J. Comp. Phys. 335 (2017), 497–515.10.1016/j.jcp.2017.01.029Search in Google Scholar

[21] Mittal, R., and Iaccarino, G. Immersed boundary methods. Annu. Rev. Fluid Mech. 37 (2005), 239–261.10.1146/annurev.fluid.37.061903.175743Search in Google Scholar

[22] Peskin, C. The immersed boundary method. Acta Numer. 11 (2002), 479–517.10.1017/S0962492902000077Search in Google Scholar

[23] Shin, D., Jeon, Y., and Park, E.-J. A novel hybrid difference method for an elliptic equation. Applied Mathematics and Computation 415 (2022).10.1016/j.amc.2021.126702Search in Google Scholar

[24] Ying, W., and Henriquez, C. A kernel-free boundary integral method for elliptic boundary value problems. J. Comput. Phys. 227 (2007), 1046–1074.10.1016/j.jcp.2007.08.021Search in Google Scholar PubMed PubMed Central

[25] Ying, W., and Wang, W.-C. A kernel-free boundary integral method for variable coefficient elliptic pdes. Comm. Comput. Phys. 15 (2014), 1108–1140.10.4208/cicp.170313.071113sSearch in Google Scholar

[26] Zhou, Y. C., S. Zhao, M. F., and Wei, G. W. High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources. J. Comput. Phys. 213 (2006), 1–30.10.1016/j.jcp.2005.07.022Search in Google Scholar

[27] Zhou, Y. C., and Wei, G. W. On the fictitious-domain and interpolation formulations of the matched interface and boundary (mib) method. J. Comput. Phys. 219 (2006), 228–246.10.1016/j.jcp.2006.03.027Search in Google Scholar