An immersed interface method for Pennes bioheat transfer equation

Champike Attanayake; So-Hsiang Chou

doi:10.3934/dcdsb.2015.20.323

Article Contents

2015, Volume 20, Issue 2: 323-337. Doi: 10.3934/dcdsb.2015.20.323

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An immersed interface method for Pennes bioheat transfer equation

Champike Attanayake^1, and
So-Hsiang Chou^2,

1.
Department of Mathematics, Miami University, Middletown OH, 45042
2.
Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43402-0221

Received: September 30, 2013

Revised: April 30, 2014

Published: February 2015

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Abstract

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.

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Mathematics Subject Classification: Primary: 65N15, 65N30; Secondary: 35J60.

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