A mixed finite element method for a nonlinear Dirichlet problem

Abstract

We study a mixed finite element approximation of a nonlinear Dirichlet problem in both two and three dimensions. This study is a first step towards the treatment of Ladyzhenskaya flows or quasi-Newtonian flows obeying the power law by mixed finite element methods. We give existence and uniqueness results for the continuous problem and its approximation and we prove an error bound.