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In this note we suggest an improvement for a family of hp-adaptive finite element methods. We point out the necessity of the new procedure by constructing model problems for which certain standard hp-adaptive algorithms fail to work properly. It is verified also in the corresponding simulations that the algorithm can terminate even though the numerical solution still contains a sizable computational error. 2010 Mathematics Subject Classification: 65N30

A note on reference solution based $hp$-adaptive PDE solvers