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An immersed linear finite element method with interface flux capturing recovery
1. | Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43402-0221, United States |
References:
[1] |
S.-H. Chou and S. Tang, Conservative $P1$ conforming and nonconforming Galerkin FEMs: Effective flux evaluation via a nonmixed method approach, SIAM J. Numer. Anal., 38 (2000), 660-680.
doi: 10.1137/S0036142999361517. |
[2] |
X. He, "Bilinear Immersed Finite Elements for Interface Problems," Ph.D thesis, Virginia Tech., Blacksberg, VA, 2009. |
[3] |
Z. Li, The immersed interface method using a finite element formulation, Applied Numerical Mathemtics, 27 (1998), 253-267.
doi: 10.1016/S0168-9274(98)00015-4. |
[4] |
Z. Li and K. Ito, "The Immersed Interface Method: Numerical Solutions of PDEs Involving Interfaces and Irregular Domains," Frontiers in Applied Mathematics, 33, SIAM, Philadelphia, PA, 2006. |
[5] |
Z. Li, T. Lin, Y. Lin and R. C. Rogers, An immersed finite element space and its approximation capability, Numer. Methods. Partial Differential Equation, 20 (2004), 338-367.
doi: 10.1002/num.10092. |
[6] |
Z. Li, T. Lin and X. Wu, New Cartesian grid methods for interface problems using the finite element formulation, Numer. Math., 96 (2003), 61-98.
doi: 10.1007/s00211-003-0473-x. |
[7] |
T. Lin, Y. Lin, R. Rogers and M. L. Ryan, A rectangular immersed finite element space for interface problems, in "Scientific Computing and Applications" (Kananaskis, AB, 2000), Advances in Computation: Theory and Practice, 7, Nova Sci. Publ., Huntington, NY, (2001), 107-114. |
show all references
References:
[1] |
S.-H. Chou and S. Tang, Conservative $P1$ conforming and nonconforming Galerkin FEMs: Effective flux evaluation via a nonmixed method approach, SIAM J. Numer. Anal., 38 (2000), 660-680.
doi: 10.1137/S0036142999361517. |
[2] |
X. He, "Bilinear Immersed Finite Elements for Interface Problems," Ph.D thesis, Virginia Tech., Blacksberg, VA, 2009. |
[3] |
Z. Li, The immersed interface method using a finite element formulation, Applied Numerical Mathemtics, 27 (1998), 253-267.
doi: 10.1016/S0168-9274(98)00015-4. |
[4] |
Z. Li and K. Ito, "The Immersed Interface Method: Numerical Solutions of PDEs Involving Interfaces and Irregular Domains," Frontiers in Applied Mathematics, 33, SIAM, Philadelphia, PA, 2006. |
[5] |
Z. Li, T. Lin, Y. Lin and R. C. Rogers, An immersed finite element space and its approximation capability, Numer. Methods. Partial Differential Equation, 20 (2004), 338-367.
doi: 10.1002/num.10092. |
[6] |
Z. Li, T. Lin and X. Wu, New Cartesian grid methods for interface problems using the finite element formulation, Numer. Math., 96 (2003), 61-98.
doi: 10.1007/s00211-003-0473-x. |
[7] |
T. Lin, Y. Lin, R. Rogers and M. L. Ryan, A rectangular immersed finite element space for interface problems, in "Scientific Computing and Applications" (Kananaskis, AB, 2000), Advances in Computation: Theory and Practice, 7, Nova Sci. Publ., Huntington, NY, (2001), 107-114. |
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