C. Ortner, D. Praetorius:

"On the convergence of adaptive nonconforming finite element methods for a class of convex variational problems";

in: "ASC Report 25/2008", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2008, ISBN: 978-3-902627-01-8.

We formulate and analyze an adaptive non-conforming finite-element

method for the solution of convex variational problems. The class of

minimization problems we admit includes highly singular problems for

which no Euler-Lagrange equation (or inequality) is available. As a

consequence, our arguments only use the structure of the energy

functional. We are nevertheless able to prove convergence of an adaptive

algorithm, despite using refinement indicators which are not reliable

error indicators.

http://www.asc.tuwien.ac.at/preprint/2008/asc25x2008.pdf

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