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M. Feischl, T. Führer, D. Praetorius:
"Quasi-optimal AFEM for non-symmetric operators";
Talk: The 12th European Finite Element Fair, Wien; 05-29-2014 - 05-30-2014.

In our talk, we analyze adaptive mesh-refinement for conforming FEM of general linear, elliptic,
second-order PDEs.
For a given conforming simplicial mesh, we allow continuous and piecewise polynomials of arbitrary, but fixed polynomial order with homogeneous boundary conditions as ansatz functions. As e.g. in [Cascon-Kreuzer-Nochetto-Siebert, SINUM 2008], adaptivity is driven by the residual error estimator, and we prove convergence even with quasi-optimal algebraic convergence rates.

The advantages over the state of the art read as follows: Unlike prior works for linear non-symmetric operators, e.g. [Cascon-Nochetto, IMA JNA 2012], our
analysis avoids the artificial quasi-symmetry assumptions
as well as the interior node property for the refinement. Moreover, the differential operator
has to satisfy a Garding inequality only. If the operator is uniformly
elliptic, no additional assumption on the initial mesh is posed. Finally, our
analysis also covers certain nonlinear problems in the frame of strongly monotone operators.