Wolfgang,
>You mean ||u-u_h||_{H^1} \le Cp || u - I_hu || \le Cp Ci h || u
||_{H^2} where Ci is an interpolation constant and Cp is an approximation
constant?
yes, exactly.
> How do you intend to evaluate the right hand side here? If you approximate
the second derivatives of u on the right hand side using jumps of normal
components of the gradient across cell faces then you get exactly the Kelly
estimator.
yes, however Kelly method is just one of possible choices. A simplest one
can be norm of hessian. also it is possible to include geometric properties
of elements plus hessian invarients to make estimator more smart (of course
specifically for each element type), it should be simple at least for linear
elements, e.g. look at seris of works by W. Cao, started by this one:
http://dx.doi.org/10.1137/S0036142903433492
but such methods is more limited to anisotropic refinement literature and
this make me curious about reason!
Cheers
RT
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