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Quasi-Optimal Convergence Rate of an AFEM for Quasi-Linear Problems of Monotone Type
We prove the quasi-optimal convergence of a standard adaptive finite element method (AFEM) for a class of nonlinear elliptic second-order equations of monotone type.The adaptive algorithm is based on residual-type a posteriori error estimators and Dörfler's strategy is assumed for marking.We first prove a contraction property for a suitable definition …