Estimates for the accuracy of the projection-difference method for an abstract hyperbolic-parabolic system like systems of thermoelasticity equations (Q610384)

The author considers a Cauchy problem for a system of abstract differential equations in a Hilbert space. This system consists of a hyperbolic and a parabolic equation, and it generalizes certain coupled equations arising, e.g., in thermoelasticity. A general numerical scheme for the solution of this problem is considered. The numerical method is based on a combination of a Galerkin method in the space variables and a finite difference method with respect to time. In particular, error estimates in the energy norm are provided for this numerical method.