Discontinuous Galerkin Finite Element Approximation of Nonlinear Second-Order Elliptic and Hyperbolic Systems

We develop the convergence analysis of discontinuous Galerkin finite element approximations to second-order quasilinear elliptic and hyperbolic systems of partial differential equations of the form, respectively, $-\sum_{\alpha=1}^d \partial_{x_\alpha} S_{i\alpha}(\nabla u(x)) = f_i(x)$, $i=1,\dots,...