Generalized difference methods for a nonlinear Dirichlet problem. (English) Zbl 0626.65091

Li, Ronghua

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

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