A continuous finite element method to approximate Friedrichs' systems isproposed and analyzed. Stability is achieved by penalizing the jumpsacross meshinterfaces of the normal derivative of some components of the discrete solution. The convergence analysis leads to optimal convergence ratesin the graph norm and suboptimal of order ½ convergence rates inthe L 2-norm. A variant of the method specialized toFriedrichs' systems associated with elliptic PDE's in mixed form andreducing the number of nonzero entries in the stiffness matrix is alsoproposed and analyzed. Finally, numerical results are presented to illustrate thetheoretical analysis.
