2,313 research outputs found
Conjugacy of 2-spherical subgroups of Coxeter groups and parallel walls
Let (W,S) be a Coxeter system of finite rank (ie |S| is finite) and let A be
the associated Coxeter (or Davis) complex. We study chains of pairwise parallel
walls in A using Tits' bilinear form associated to the standard root system of
(W,S). As an application, we prove the strong parallel wall conjecture of G
Niblo and L Reeves [J Group Theory 6 (2003) 399--413]. This allows to prove
finiteness of the number of conjugacy classes of certain one-ended subgroups of
W, which yields in turn the determination of all co-Hopfian Coxeter groups of
2--spherical type.Comment: This is the version published by Algebraic & Geometric Topology on 14
November 200
Finite element differential forms on curvilinear cubic meshes and their approximation properties
We study the approximation properties of a wide class of finite element
differential forms on curvilinear cubic meshes in n dimensions. Specifically,
we consider meshes in which each element is the image of a cubical reference
element under a diffeomorphism, and finite element spaces in which the shape
functions and degrees of freedom are obtained from the reference element by
pullback of differential forms. In the case where the diffeomorphisms from the
reference element are all affine, i.e., mesh consists of parallelotopes, it is
standard that the rate of convergence in L2 exceeds by one the degree of the
largest full polynomial space contained in the reference space of shape
functions. When the diffeomorphism is multilinear, the rate of convergence for
the same space of reference shape function may degrade severely, the more so
when the form degree is larger. The main result of the paper gives a sufficient
condition on the reference shape functions to obtain a given rate of
convergence.Comment: 17 pages, 1 figure; v2: changes in response to referee reports; v3:
minor additional changes, this version accepted for Numerische Mathematik;
v3: very minor updates, this version corresponds to the final published
versio
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