A Galerkin method for a nonlinear Dirichlet problem

A Galerkin method due to Nitsche for treating the Dirichlet problem for a linear second-order elliptic equation is extended to cover the nonlinear equation V • (a(x, m)Vm) = /. The asymptotic error estimates are of the same form as in the linear case. Newton's method can be used to solve the nonlinear algebraic equations.