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M. Feischl, T. Führer, D. Praetorius:
"Adaptive FEM with optimal convergence rates for a certain class of non-symmetric and possibly non-linear problems";
SIAM Journal on Numerical Analysis, 52 (2014), 2; S. 601 - 625.

We analyze adaptive mesh-refining algorithms for conforming finite element discretizations
of certain non-linear second-order partial differential equations. We allow continuous
polynomials of arbitrary, but fixed polynomial order. The adaptivity is driven by the residual
error estimator. We prove onvergence even with optimal algebraic convergence rates. In
particular, our analysis covers general linear second-order elliptic operators. Unlike prior
works for linear non-symmetric operators, our analysis avoids the interior node property for
the refinement, and the differential operator has to satisfy a Garding inequality only. If the
differential operator is uniformly elliptic, no additional assumption on the initial mesh is posed.

adaptive algorithm, convergence, optimal cardinality

http://dx.doi.org/10.1137/120897225

http://publik.tuwien.ac.at/files/PubDat_222557.pdf