Abstract
We present a posteriori error estimates for nonlinear stationary problems departing from an abstract result which establishes the basic equivalence of error and residual. The main tool is the implicit function theorem along with modifications for bifurcation and turning points. We apply the abstract results to quasilinear elliptic equations and the stationary incompressible Navier–Stokes equations. The nonlinear approach also enables us to efficiently treat linear elliptic eigenvalue problems.
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