Stabilization Techniques in Finite Element Discretizations for Moment Approximations

The paper is concerned with the discretization of a linearized subsystem of the regularized 13-moment equations. These equations state an approximation of the Boltzmann equation as a result of applying moment methods. First, the derivation of the linearized equations is outlined, followed by the introduction of the numerical approach. The subsystem is of elliptic nature which makes finite elements the method of choice. The handling of saddle-point structures within the equations and non-standard boundary conditions are discussed. In this context, the concept of stabilization is presented and applied to the specific problem.