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Adaptive higher-order finite element methods ($hp$-FEM) are well known for their potential of exceptionally fast (exponential) convergence. However, most $hp$-FEM codes remain in an academic setting due to an extreme algorithmic complexity of $hp$-adaptivity algorithms. This paper aims at simplifying $hp$-adaptivity for $H$(curl)-conforming approximations by presenting a novel technique of arbitrary-level hanging nodes. The technique is described and it is demonstrated numerically that it makes adaptive $hp$-FEM more efficient compared to $hp$-FEM on regular meshes and meshes with one-level hanging nodes.
}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.10-m1012}, url = {http://global-sci.org/intro/article_detail/aamm/8344.html} }Adaptive higher-order finite element methods ($hp$-FEM) are well known for their potential of exceptionally fast (exponential) convergence. However, most $hp$-FEM codes remain in an academic setting due to an extreme algorithmic complexity of $hp$-adaptivity algorithms. This paper aims at simplifying $hp$-adaptivity for $H$(curl)-conforming approximations by presenting a novel technique of arbitrary-level hanging nodes. The technique is described and it is demonstrated numerically that it makes adaptive $hp$-FEM more efficient compared to $hp$-FEM on regular meshes and meshes with one-level hanging nodes.