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When reading literatures about finite element method, the term "hanging nodes" can often be encountered. Could anyone tell me what indeed is a hanging node?

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The following picture illustrates a mesh with a hanging node and a mesh containing no hanging node:

enter image description here

Usually with a finite element mesh the vertices are shared with their other neighbouring elements, but the circled node does not belong to the bottom triangle. We call this node a hanging node. This commonly occurs during the process of adaptive mesh refinement. Hanging nodes are either removed - as is done in the above picture by connecting it to another vertex and thus creating two new elements - or by imposing constraints on the system.

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  • $\begingroup$ Thanks for your detailed answer. Could you please suggest some papers or books regarding the treatment of hanging nodes, or the treatment of non-conforming elements? $\endgroup$ – user123 Nov 22 '15 at 7:19
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    $\begingroup$ @David406 Hanging node are usually removed by creating new elements - as is done in the above picture - or constraints are imposed on the system. I have only removed hanging nodes during adaptive refinement. I highly recommend Wolfgang Bangerth's video tutorials. They contain the info you are looking for in lecture 14-17?? and much much more! $\endgroup$ – James Nov 22 '15 at 7:28

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