Finite element methods for non-fourier thermal wave model of bio heat transfer with an interface

We propose a fitted finite element method for non-Fourier bio heat transfer model in multi-layered media. Specifically, we employ the Maxwell–Cattaneo equation on the physical media that have a heterogeneous conductivity. Well-posedness of the model interface problem is established. A continuous piecewise linear finite element space is employed for the spatially semidiscrete approximation and the temporal discretization is based on backward scheme. Optimal order error estimates for both semidiscrete and fully discrete schemes are proved in L∞(H1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{\infty }(H^1)$$\end{document} norm. Finally, we give numerical examples to verify our theoretical results. The new results and finite element schemes can be applied in the fields of engineering, medicine, and biotechnology.