Error estimates for discontinuous Galerkin method for nonlinear parabolic equations (Q819034)

The authors obtain an optimal error estimate in the \(L^\infty(L^2)\) norm for the discontinuous Galerkin approximation using a penalty term for the following nonlinear parabolic equation \[ u_t - \nabla \cdot (a(x,u) \nabla u) = f(x,u), \quad (x,t) \in \Omega \times (0,T], \] with boundary condition \[ a(x,u) \nabla u \cdot n = 0, \quad (x,t) \in \partial \Omega \times (0,T]. \]