TY - JOUR T1 - Adaptive $hp$-FEM with Arbitrary-Level Hanging Nodes for Maxwell's Equations AU - Solin , Pavel AU - Dubcova , Lenka AU - Dolezel , Ivo JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 518 EP - 532 PY - 2010 DA - 2010/02 SN - 2 DO - http://doi.org/10.4208/aamm.10-m1012 UR - https://global-sci.org/intro/article_detail/aamm/8344.html KW - AB -

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.