M. Feischl, T. Führer, D. Praetorius:

"Adaptive FEM with optimal convergence rates for a certain class of non-symmetric and possibly non-linear problems";

in: "ASC Report 43/2012", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2012, ISBN: 978-3-902627-05-6, 1 - 21.

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://www.asc.tuwien.ac.at/preprint/2012/asc43x2012.pdf

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