“…where τ is an appropriate constant, e.g., τ = f 0,T . This modification of the artificial diffusion allows for the upper and lower bounds of the corresponding local nonlinear operator D T (•;•,•), hence the existence, stability, and convergence of discrete solutions follow by using similar approaches in the analysis of nonlinear finite element methods; see [3,11,39,42,49]. We note that the choice of the artificial diffusion (ξ T (u h ) on each element) is determined by the artificial dissipation term β b , and β b is obtained by minimizing the kinetic energy E k .…”