Discrete models in the dynamic problem of linear elasticity and conservation laws

The dynamic problem of linear elasticity (a continuous model) is based on the momentum and moment of momentum conservation laws and hence has an additional conservation law for the total energy (the kinetic plus potential energy). Continuous models with this property are referred to as entropy models (S.K. Godunov). For difference schemes, this property is described with the use of the notion of complete conservativeness) (A.A. Samarskii). For the considered problem, we make a complete analysis of a two-parameter family of “conjugatecoordinated” two-layer difference schemes including a conservative scheme. For the latter, we construct efficient triangular-factorized implementations with the same parallelism degree as in ordinary explicit schemes. For difference schemes without the property of complete conservativeness, we discuss the role of the law of passage to the limit for the minimization of imbalance in the total energy.