Li, Ronghua Generalized difference methods for a nonlinear Dirichlet problem. (English) Zbl 0626.65091 SIAM J. Numer. Anal. 24, 77-88 (1987). The nonlinear problem studied is \(-\Delta (a(x,y,u)\Delta u)=f(x,y)\) in a domain D, \(u(x,y)=0\) on \(\partial D\), where D is a bounded domain, a is twice continuously differentiable with bounded derivatives through the second order. Generalized difference methods are defined, the existence of the approximate solution is established as is the error estimate for the approximate solution. Reviewer: W.Ames Cited in 47 Documents MSC: 65N06 Finite difference methods for boundary value problems involving PDEs 65N15 Error bounds for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35J65 Nonlinear boundary value problems for linear elliptic equations Keywords:second order nonlinear elliptic equations; Galerkin method; generalized difference method; test space; trial space; interpolating projection; difference methods; error estimate PDF BibTeX XML Cite \textit{R. Li}, SIAM J. Numer. Anal. 24, 77--88 (1987; Zbl 0626.65091) Full Text: DOI OpenURL