Hodge Decomposition Methods for a Quad-Curl Problem on Planar Domains
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Scientific Computing"
DOI: 10.1007/s10915-017-0449-0
Abstract: We develop and analyze $$P_k$$Pk Lagrange finite element methods for a quad-curl problem on planar domains that is based on the Hodge decomposition of divergence-free vector fields. Numerical results that illustrate the performance of the… read more here.
Keywords: planar domains; hodge decomposition; methods quad; curl problem ... See more keywords
Besov and Triebel–Lizorkin regularity for the Hodge decomposition and applications to magnetic potentials
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2016.07.070
Abstract: Abstract The Hodge decomposition is a fundamental result in the theory of differential forms. It has been extensively studied from different perspectives and it is the source of several applications in physics and mathematics. For… read more here.
Keywords: hodge decomposition; regularity; magnetic potentials; besov triebel ... See more keywords
Hodge decomposition of wall shear stress vector fields characterizing biological flows
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DOI: 10.1098/rsos.181970
Abstract: A discrete boundary-sensitive Hodge decomposition is proposed as a central tool for the analysis of wall shear stress (WSS) vector fields in aortic blood flows. The method is based on novel results for the smooth… read more here.
Keywords: vector; hodge decomposition; wall shear; shear stress ... See more keywords
Meshless Approximation and Helmholtz-Hodge Decomposition of Vector Fields
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DOI: 10.1109/tvcg.2020.3016588
Abstract: The analysis of vector fields is crucial for the understanding of several physical phenomena, such as natural events (e.g., analysis of waves), diffusive processes, electric and electromagnetic fields. While previous work has been focused mainly… read more here.
Keywords: meshless approximation; helmholtz hodge; vector fields; hodge decomposition ... See more keywords