Dear all,
in step 9 it is stated that if solution be H1, then we may have lowwer dimensional singularites and concentration of grid near them without reduction of estimator (if we use 2nd derivative based error estimators). My question: - which kind of estimator we should use in this cases? - it seems that refinment around singularity is a feasible, becasue we have concentration of information around them, e.g. when we have a point singularity be refinement we explore details of local solution structure, so we expct decrease of l2-norm, though estimator does not decrease, also at least most of estimators refine grid in the vicinity of singularities, any comment on this issue? - why estimator does not decrease? because at least (theoritically) we compute a measure of estimator inside grid and so lower dimansional features can not have contribution in integral, am i miss something? also i have another kind question: it is well known that (at least proved for some specific problems) interpolation error make a bound for discritization error, so it can be considered as an error estimator (though is not very common, else for anisotorpic refinement), what is drawback of using such estimations? Cheers RT
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