2021/04/28 by Lars Diening, Johannes Storn, Tabea Tscherpel · 1 citation
Chemistry · Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Bubble #Chemistry #Combinatorics #Counterexample #Dimension (graph theory) #Divergence (linguistics) #Element (criminal law) #Finite element method #Mathematical analysis #Mathematics #Mechanics #Numerical methods in engineering #Operator (biology) #Physics #Taylor series #cs.NA #math.NA #msc:65N12 #msc:65N30 #msc:76D07
paper · pdf · doi:10.1007/s00211-021-01260-1
14 pages
arxiv created 2021/04/28 · openalex publication_date 2021/12/18 · arxiv updated 2021/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Abstract We design a local Fortin operator for the lowest-order Taylor–Hood element in any dimension, which was previously constructed only in 2D. In the construction we use tangential edge bubble functions for the divergence correcting operator. This naturally leads to an alternative inf-sup stable reduced finite element pair. Furthermore, we provide a counterexample to the inf-sup stability and hence to existence of a Fortin operator for the P2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>P</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> – P0 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>P</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> and the augmented Taylor–Hood element in 3D.