Pousin, J.Rappaz, J.2006-08-242006-08-242006-08-24199410.1007/s002110050088https://infoscience.epfl.ch/handle/20.500.14299/233691WOS:A1994PZ75100006In an abstract framework we present a formalism which specifies the notions of consistency and stability of Petrov-Galerkin methods used to approximate nonlinear problems which are, in many practical situations, strongly nonlinear elliptic problems. This formalism gives rise to a priori and a posteriori error estimates which can be used for the refinement of the mesh in adaptive finite element methods applied to elliptic nonlinear problems. This theory is illustrated with the example: -div (k(u)DELTAu) + c. DELTAu = f in a two dimensional domain OMEGA with Dirichlet boundary conditions.text::journal::journal article::research article