Nonconformal finite element schemes for hyperbolic linear systems of equations

In this paper we propose a variant of nonconformal finite element method of approximation of the multidimensional linear first order hyperbolic system. The approach is used that was suggested earlier for the scalar convection-diffusion equation, based on Galerkin–Petrov approximation for the mixed formulation of the original problem, taking into account the direction of convection. Using this approach for the approximation of symmetric systems of equations allows naturally to take into account the local direction of the characteristics, as well as preserve the basic properties of the spatial operator of the original problem.
Unconditional stability of the semidiscrete scheme, implicit two-layer difference schemes with weights is proved.