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It is necessary for me to solve a Poisson equation by adaptive finite element method with transition elements technique to get conforming mesh. For the first local refinement everything is OK, because there is not any transition elements, but after that there are some of them. After the first step, the error must be estimated on these elements or no? If yes, maybe the error is large and the transition element must be refine in the next refinement, so they are not transition, if no, this means some parts of domain are without error estimation, or I should find the error on larger elements without considere to hanging nodes?

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You will need to estimate the error on all cells, including transition cells. You may then wish to refine these differently, if necessary -- see for example the Red-Green Strategy (which I explain in more detail in lecture 15 at http://www.math.tamu.edu/~bangerth/videos.html).

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