Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems I: The scalar case - Houston, P; Robson, J; Suli, E (Unspecified, 2004)
We develop a one--parameter family of hp-version discontinuous Galerkin finite element methods for the numerical solution of quasilinear elliptic equations in divergence-form in a bounded Lipschitz domain. Using Brouwer's Fixed Point Theorem, we show existence and uniqueness of the solution. In addition, we derive an error bound in a broken energy norm which is optimal in h and mildly suboptimal in p.