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An immersed interface method for Pennes bioheat transfer equation
1. | Department of Mathematics, Miami University, Middletown OH, 45042, United States |
2. | Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43402-0221 |
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] |
S. H. Chou, An immersed linear finite element method with interface flux capturing recovery, Discrete and Continuous Dynamical Systems-Series-B, 17 (2012), 2343-2357.
doi: 10.3934/dcdsb.2012.17.2343. |
[3] |
W. Dai, H. Yu and R. Nassar, A forth order compact finite-difference scheme for solving a 1-D Pennes bioheat transfer equation in a tripple layered skin structure, Numerical Heat Transfer, 46 (2004), 447-461. |
[4] |
W. Dai, H. Yu and R. Nassar, Optimal temperature distribution in a three dimensional triple layered skin structure embedded with artery and vein vasculature, Num. Heat Transfer, 50 (2006), 809-834. |
[5] |
Z. S. Deng and J. Liu, Mathematical modeling of temperature mapping over skin surface and its implementation in thermal disease diagnostics, Comput. Biol. Med., 34 (2004), 495-521.
doi: 10.1016/S0010-4825(03)00086-6. |
[6] |
X. He, T. Lin and Y. Lin, Immersed finite element methods for elliptic interface problems with non-Homogeneous jump conditions, Inter. J. Numerical Analysis and Modeling, 8 (2011), 284-301. |
[7] |
S. C. Jiang, N. Ma and H. J. Li, Effects of thermal properties and geometrical dimensions on skin burn injuries, Burns, 28 (2002), 713-717.
doi: 10.1016/S0305-4179(02)00104-3. |
[8] |
Z. Li, The immersed interface method using a finite element formulation, Applied Numerical Mathematics, 27 (1998), 253-267.
doi: 10.1016/S0168-9274(98)00015-4. |
[9] |
Z. Li, T. Lin, Y. Lin and R. C. Rogers, An immersed finite element space and its approximation capability, Numer. Methods. Partial Differential Equations, 20 (2004), 338-367.
doi: 10.1002/num.10092. |
[10] |
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. |
[11] |
T. Lin, Y. Lin and W. Sun, Error estimation of a class quadratic immersed finite element methods for elliptic interface problems, Discrete and Continuous Dynamical Systems Series-B, 7 (2007), 807-823.
doi: 10.3934/dcdsb.2007.7.807. |
[12] |
E. H. Liu, G. M. Saidel and H. Harasaki, Model analysis of tissue responses totransient and chronic heating, Ann. Biomed. Eng, 31 (2003), 1007-1048. |
[13] |
H. H. Pennes, Analysis of tissue and arterial blood temperature in the resting forearm, J. Appl. Physiol., 1 (1948), 93-122. |
[14] |
V. Thomee, Galerkin Finite Element Methods for Parabolic Problems, Springer, 2006. |
[15] |
D. A. Tori and J. D. Dale, A finite element model of skin subjected to a flasf fire, J. Biomed Eng., 116 (1994), 250-255. |
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] |
S. H. Chou, An immersed linear finite element method with interface flux capturing recovery, Discrete and Continuous Dynamical Systems-Series-B, 17 (2012), 2343-2357.
doi: 10.3934/dcdsb.2012.17.2343. |
[3] |
W. Dai, H. Yu and R. Nassar, A forth order compact finite-difference scheme for solving a 1-D Pennes bioheat transfer equation in a tripple layered skin structure, Numerical Heat Transfer, 46 (2004), 447-461. |
[4] |
W. Dai, H. Yu and R. Nassar, Optimal temperature distribution in a three dimensional triple layered skin structure embedded with artery and vein vasculature, Num. Heat Transfer, 50 (2006), 809-834. |
[5] |
Z. S. Deng and J. Liu, Mathematical modeling of temperature mapping over skin surface and its implementation in thermal disease diagnostics, Comput. Biol. Med., 34 (2004), 495-521.
doi: 10.1016/S0010-4825(03)00086-6. |
[6] |
X. He, T. Lin and Y. Lin, Immersed finite element methods for elliptic interface problems with non-Homogeneous jump conditions, Inter. J. Numerical Analysis and Modeling, 8 (2011), 284-301. |
[7] |
S. C. Jiang, N. Ma and H. J. Li, Effects of thermal properties and geometrical dimensions on skin burn injuries, Burns, 28 (2002), 713-717.
doi: 10.1016/S0305-4179(02)00104-3. |
[8] |
Z. Li, The immersed interface method using a finite element formulation, Applied Numerical Mathematics, 27 (1998), 253-267.
doi: 10.1016/S0168-9274(98)00015-4. |
[9] |
Z. Li, T. Lin, Y. Lin and R. C. Rogers, An immersed finite element space and its approximation capability, Numer. Methods. Partial Differential Equations, 20 (2004), 338-367.
doi: 10.1002/num.10092. |
[10] |
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. |
[11] |
T. Lin, Y. Lin and W. Sun, Error estimation of a class quadratic immersed finite element methods for elliptic interface problems, Discrete and Continuous Dynamical Systems Series-B, 7 (2007), 807-823.
doi: 10.3934/dcdsb.2007.7.807. |
[12] |
E. H. Liu, G. M. Saidel and H. Harasaki, Model analysis of tissue responses totransient and chronic heating, Ann. Biomed. Eng, 31 (2003), 1007-1048. |
[13] |
H. H. Pennes, Analysis of tissue and arterial blood temperature in the resting forearm, J. Appl. Physiol., 1 (1948), 93-122. |
[14] |
V. Thomee, Galerkin Finite Element Methods for Parabolic Problems, Springer, 2006. |
[15] |
D. A. Tori and J. D. Dale, A finite element model of skin subjected to a flasf fire, J. Biomed Eng., 116 (1994), 250-255. |
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