Numerical analysis of a dual-phase-lag model with microtemperatures

In the last twenty years, analysis of problems involving dual-phase-lag models has received an increasing attention. this work, we consider coupling between one these and microtemperatures effects. order to overcome infinite speed paradox, two relaxation parameters are introduced for each evolution equation related temperature microtemperatures, leading a system linear hyperbolic partial differential equations. Its variational formulation is written in terms acceleration acceleration. An energy decay property proved. Next, fully discrete approximations by using finite element method Euler scheme, proving stability version decay, obtaining priori error estimates performing one- two-dimensional numerical simulations.