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A Posteriori Existence in Numerical Computations

A typical a posteriori error analysis for numerical methods for differential equations consists of two elements: the stability of the continuous problem and an a posteriori computed residual estimate. If the problem is nonlinear, then this is possible only if it is strongly monotone. In this paper, we will estimate the stability constant a posteriori as well, in order to apply the inverse function theorem to derive the existence of solutions from the numerical computation, and thus obtain rigorous a posteriori error estimates for nonmonotone equations.