Convergence of finite element methods for hyperbolic heat conduction model with an interface

The paper concerns numerical study of non-Fourier bio heat transfer model in multi-layered media. Specifically, we employ the Maxwell–Cattaneo equation on the physical media with discontinuous coefficients. A fitted finite element method is proposed and analyzed for a hyperbolic heat conduction model with discontinuous coefficients. Typical semidiscrete and fully discrete schemes are presented for a fitted finite element discretization with straight interface triangles. The fully discrete space–time finite element discretizations are based on second order in time Newmark scheme. Optimal a priori error estimates for both semidiscrete and fully discrete schemes are proved in L ∞ ( L 2 ) norm. Numerical experiments are reported for several test cases to confirm our theoretical convergence rate. Finite element algorithm presented here can be used to solve a wide variety of hyperbolic heat conduction models for non-homogeneous inner structures.