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Quasi-optimal convergence rate of an AFEM for quasi-linear problems of monotone type

2012
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Numerical Mathematics: Theory, Methods and Applications
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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 of total error, analogous to the one used by Diening and Kreuzer [6] and equivalent to the total error defined by Cascón et al. [2] . This

doi:10.4208/nmtma.2012.m1023
fatcat:jqdhm2imizcopa6hvoisnkfs2a