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 - <p style="text-align: justify;">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.</p>