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An augmented immersed interface method for moving structures with mass
Error estimation for immersed interface solutions
1. | Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC V6T 1Z2, Canada |
2. | Nanoscale and Reactive Processes, Sandia National Laboratories, Albuquerque, NM 87185-0836, United States |
3. | Department of Mathematics, Tulane University, 6823 St. Charles Ave., New Orleans, LA 70118, United States |
References:
[1] |
W. Auzinger, Defect correction for nonlinear elliptic difference equations,, Numerische Mathematik, 51 (1987), 199.
doi: 10.1007/BF01396749. |
[2] |
R. LeVeque and Z. Li, The immersed interface method for elliptic equations with discontinuous coefficients and singular sources,, SIAM Journal on Numerical Analysis, 31 (1994), 1019.
doi: 10.1137/0731054. |
[3] |
R. LeVeque, "Finite Difference Methods for Ordinary and Partial Differential Equations. Steady-State and Time-Dependent Problems,", SIAM, (2007).
|
[4] |
Z. Li, A fast iterative algorithm for elliptic interface problems,, SIAM Journal on Numerical Analysis, 35 (1998), 230.
doi: 10.1137/S0036142995291329. |
[5] |
Z. Li and M.-C. Lai, The immersed interface method for Navier-Stokes equations with singular forces,, Journal of Computational Physics, 171 (2001), 822.
doi: 10.1006/jcph.2001.6813. |
[6] |
Z. Li and K. Ito, Maximum principle preserving schemes for interface problems with discontinuous coefficients,, SIAM Journal on Scientific Computing, 23 (2001), 339.
doi: 10.1137/S1064827500370160. |
[7] |
Z. Li and K. Ito, "The Immersed Interface Method. Numerical Solutions of PDE's Involving Interfaces and Irregular Domains,", Frontiers in Applied Mathematics, 33 (2006).
|
[8] |
B. Lindberg, Error estimation and iterative improvement for discretization algorithms,, BIT, 20 (1980), 486.
doi: 10.1007/BF01933642. |
[9] |
W. Oberkampf and C. Roy, "Verification and Validation in Scientific Computing,", Cambridge University Press, (2010). Google Scholar |
[10] |
C. Peskin, The immersed boundary method,, Acta Numerica, 11 (2002), 479.
doi: 10.1017/S0962492902000077. |
[11] |
C. Pozrikidis, "Boundary Integral and Singularity Methods for Linearized Viscous Flow,", Cambridge Texts in Applied Mathematics, (1992).
doi: 10.1017/CBO9780511624124. |
[12] |
P. Roache, "Verification and Validation in Computational Science and Engineering,", Hermosa Publishers, (1998). Google Scholar |
[13] |
C. Roy, A. Raju and M. Hopkins, Estimation of discretization errors using the method of nearby problems,, AIAA Journal, 45 (2007), 1232.
doi: 10.2514/1.24282. |
[14] |
C. Roy and A. Sinclair, On the generation of exact solutions for evaluating numerical schemes and estimating discretization error,, Journal of Computational Physics, 228 (2009), 1790.
doi: 10.1016/j.jcp.2008.11.008. |
[15] |
H. Stetter, The defect correction principle and discretization methods,, Numerische Mathematik, 29 (): 425.
doi: 10.1007/BF01432879. |
[16] |
S. Xu and Z. Wang, An immersed interface method for simulating the interaction of a fluid with moving boundaries,, Journal of Computational Physics, 216 (2006), 454.
doi: 10.1016/j.jcp.2005.12.016. |
[17] |
X. Zhong, A new high-order immersed interface method for solving elliptic equations with imbedded interface of discontinuity,, Journal of Computational Physics, 225 (2007), 1066.
doi: 10.1016/j.jcp.2007.01.017. |
[18] |
Y. Zhou, S. Zhou, M. Feig and G. Wei, High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources,, Journal of Computational Physics, 213 (2006), 1.
doi: 10.1016/j.jcp.2005.07.022. |
show all references
References:
[1] |
W. Auzinger, Defect correction for nonlinear elliptic difference equations,, Numerische Mathematik, 51 (1987), 199.
doi: 10.1007/BF01396749. |
[2] |
R. LeVeque and Z. Li, The immersed interface method for elliptic equations with discontinuous coefficients and singular sources,, SIAM Journal on Numerical Analysis, 31 (1994), 1019.
doi: 10.1137/0731054. |
[3] |
R. LeVeque, "Finite Difference Methods for Ordinary and Partial Differential Equations. Steady-State and Time-Dependent Problems,", SIAM, (2007).
|
[4] |
Z. Li, A fast iterative algorithm for elliptic interface problems,, SIAM Journal on Numerical Analysis, 35 (1998), 230.
doi: 10.1137/S0036142995291329. |
[5] |
Z. Li and M.-C. Lai, The immersed interface method for Navier-Stokes equations with singular forces,, Journal of Computational Physics, 171 (2001), 822.
doi: 10.1006/jcph.2001.6813. |
[6] |
Z. Li and K. Ito, Maximum principle preserving schemes for interface problems with discontinuous coefficients,, SIAM Journal on Scientific Computing, 23 (2001), 339.
doi: 10.1137/S1064827500370160. |
[7] |
Z. Li and K. Ito, "The Immersed Interface Method. Numerical Solutions of PDE's Involving Interfaces and Irregular Domains,", Frontiers in Applied Mathematics, 33 (2006).
|
[8] |
B. Lindberg, Error estimation and iterative improvement for discretization algorithms,, BIT, 20 (1980), 486.
doi: 10.1007/BF01933642. |
[9] |
W. Oberkampf and C. Roy, "Verification and Validation in Scientific Computing,", Cambridge University Press, (2010). Google Scholar |
[10] |
C. Peskin, The immersed boundary method,, Acta Numerica, 11 (2002), 479.
doi: 10.1017/S0962492902000077. |
[11] |
C. Pozrikidis, "Boundary Integral and Singularity Methods for Linearized Viscous Flow,", Cambridge Texts in Applied Mathematics, (1992).
doi: 10.1017/CBO9780511624124. |
[12] |
P. Roache, "Verification and Validation in Computational Science and Engineering,", Hermosa Publishers, (1998). Google Scholar |
[13] |
C. Roy, A. Raju and M. Hopkins, Estimation of discretization errors using the method of nearby problems,, AIAA Journal, 45 (2007), 1232.
doi: 10.2514/1.24282. |
[14] |
C. Roy and A. Sinclair, On the generation of exact solutions for evaluating numerical schemes and estimating discretization error,, Journal of Computational Physics, 228 (2009), 1790.
doi: 10.1016/j.jcp.2008.11.008. |
[15] |
H. Stetter, The defect correction principle and discretization methods,, Numerische Mathematik, 29 (): 425.
doi: 10.1007/BF01432879. |
[16] |
S. Xu and Z. Wang, An immersed interface method for simulating the interaction of a fluid with moving boundaries,, Journal of Computational Physics, 216 (2006), 454.
doi: 10.1016/j.jcp.2005.12.016. |
[17] |
X. Zhong, A new high-order immersed interface method for solving elliptic equations with imbedded interface of discontinuity,, Journal of Computational Physics, 225 (2007), 1066.
doi: 10.1016/j.jcp.2007.01.017. |
[18] |
Y. Zhou, S. Zhou, M. Feig and G. Wei, High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources,, Journal of Computational Physics, 213 (2006), 1.
doi: 10.1016/j.jcp.2005.07.022. |
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