Abstract
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.
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