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Convergence of finite element methods for hyperbolic heat conduction model with an interface. (English) Zbl 1446.65108
Summary: 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 $$L^\infty(L^2)$$ 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.

##### MSC:
 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65M15 Error bounds for initial value and initial-boundary value problems involving PDEs 78A25 Electromagnetic theory (general) 80A10 Classical and relativistic thermodynamics 35Q79 PDEs in connection with classical thermodynamics and heat transfer
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