Optimal a priori error estimates for the finite element approximation of dual-phase-lag bio heat model in heterogeneous medium. (English) Zbl 1472.65120
Summary: Galerkin finite element method is applied to dual-phase-lag bio heat model in heterogeneous medium. Well-posedness of the model interface problem and a priori estimates of its solutions are established. Optimal a priori error estimates for both semidiscrete and fully discrete schemes are proved in \(L^\infty (L^2)\) norm. The fully discrete space-time finite element discretizations is based on second order in time Newmark scheme. Finally, numerical results for two dimensional test problems are presented in support of our theoretical findings. Finite element algorithm presented here can contribute to a variety of engineering and medical applications.
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 |
| 35L05 | Wave equation |
| 35B45 | A priori estimates in context of PDEs |
| 92C05 | Biophysics |
| 35Q79 | PDEs in connection with classical thermodynamics and heat transfer |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
Keywords:
general hyperbolic equation; heterogeneous medium; finite element method; a priori analysis; optimal error estimatesReferences:
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