# American Institute of Mathematical Sciences

March  2015, 20(2): 323-337. doi: 10.3934/dcdsb.2015.20.323

## 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

Received  October 2013 Revised  May 2014 Published  January 2015

We consider an immersed finite element method for solving one dimensional Pennes bioheat transfer equation with discontinuous coefficients and nonhomogenous flux jump condition. Convergence properties of the semidiscrete and fully discrete schemes are investigated in the $L^{2}$ and energy norms. By using the computed solution from the immerse finite element method, an inexpensive and effective flux recovery technique is employed to approximate flux over the whole domain. Optimal order convergence is proved for the immersed finite element approximation and its flux. Results of the simulation confirm the convergence analysis.
Citation: Champike Attanayake, So-Hsiang Chou. An immersed interface method for Pennes bioheat transfer equation. Discrete & Continuous Dynamical Systems - B, 2015, 20 (2) : 323-337. doi: 10.3934/dcdsb.2015.20.323
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