Partial differential-algebraic systems of second order with symmetric convection

This paper deals with initial boundary value problems (IBVPs) of linear and some semilinear partial differential algebraic equations (PDAEs) with symmetric first order (convection) terms which are semidiscretized with respect to the space variables by means of a standard conform finite element method. The aim is to give L2-convergence results for the semidiscretized systems when the finite element mesh parameter h goes to zero. In general, without the assumption of symmetry (and some further conditions) it is difficult to get such results. According to many practical applications, the PDAEs may have also hyperbolic parts. These are described by means of Friedrichs' theory for symmetric positive systems of differential equations. The PDAEs are assumed to be of time index 1.