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@MISC{,
            author = {Roub{\'{\i}}{\v c}ek, Tom{\'{a}}{\v s}},
             title = {An energy-conserving time-discretisation scheme for poroelastic media with phase-field fracture emitting waves and heat},
           journal = {AIMS’ journal “Discrete and Cont. Dynam. Syst.”},
              year = {2016},
          abstract = {The model of brittle cracks in elastic solids at small strains is approximated by the Ambrosio-Tortorelli functional and then extended into evolution situation to an evolutionary system, involving viscoelasticity,
inertia, heat transfer, and coupling with Cahn-Hilliard-type diffusion of a fluid due to Fick’s or
Darcy’s laws. Damage resulted from the approximated crack model is considered rate independent. The
fractional-step Crank-Nicolson-type time discretisation is devised to decouple the system in a way so that
the energy is conserved even in the discrete scheme. The numerical stability of such a scheme is shown,
and also convergence towards suitably defined weak solutions. Various generalizations involving plasticity,
healing in damage, or phase transformation are mentioned, too.},
  Preprint project = {NCMM},
     Preprint year = {2016},
   Preprint number = {11},
       Preprint ID = {NCMM/2016/11}
}