Related papers: H1-conforming finite element cochain complexes and…
Quasiperiodic arrangements of the constitutive materials in composites result in effective properties with very unusual electromagnetic and elastic properties. The paper discusses the cut-and-projection method that is used to characterize…
Let $W$ denote a simply-laced Coxeter group with $n$ generators. We construct an $n$-dimensional representation $\phi$ of $W$ over the finite field $F_2$ of two elements. The action of $\phi(W)$ on $F_2^n$ by left multiplication is…
We show that the cohomology ring of a finite-dimensional complex pointed Hopf algebra with an abelian group of group-like elements is finitely generated. Our strategy has three major steps. We first reduce the problem to the finite…
For a Cohen-Macaulay ring $R$, we exhibit the equivalence of the bounded derived categories of certain resolving subcategories, which, amongst other results, yields an equivalence of the bounded derived category of finite length and finite…
Given a finite modular tensor category, we associate with each compact surface with boundary a cochain complex in such a way that the mapping class group of the surface acts projectively on its cohomology groups. In degree zero, this action…
Advanced transition elements are of utmost importance in many applications of the finite element method (FEM) where a local mesh refinement is required. Considering problems that exhibit singularities in the solution, an adaptive…
This paper introduces a quasi-interpolation operator for scalar- and vector-valued finite element spaces constructed on affine, shape-regular meshes with some continuity across mesh interfaces.This operator gives optimal estimates of the…
This paper constructs a unified family of nonconforming finite element spaces for $H\Lambda^k$ in $\mathbb{R}^n$ ($0\leqslant k\leqslant n$, $n\geqslant 1$). The spaces employ piecewise Whitney forms as shape functions, and include the…
We prove refined generating series formulae for characters of (virtual) cohomology representations of external products of suitable coefficients, e.g., (complexes of) constructible or coherent sheaves, or (complexes of) mixed Hodge modules…
We summarise three applications of the obstacle problem to membrane contact, elastoplastic torsion and cavitation modelling, and show how the resulting models can be solved using mixed finite elements. It is challenging to construct fixed…
In [P. Niroomand, R. Rezaei, On the exterior degree of finite groups, Comm. Algebra 39 (2011), 335-343] it is introduced a group invariant, related to the number of elements $x$ and $y$ of a finite group $G$, such that $x \wedge y = 1_{G…
A product of cochains in a polyhedral complex is constructed. The multiplication algorithm depends on the choice of a parameter. The parameter is a linear functional on the ambient space. Cocycles form a subring of the ring of cochains,…
We construct conforming finite element elasticity complexes on Worsey-Farin splits in three dimensions. Spaces for displacement, strain, stress, and the load are connected in the elasticity complex through the differential operators…
A new framework for noncommutative complex geometry on quantum homogeneous spaces is introduced. The main ingredients used are covariant differential calculi and Takeuchi's categorical equivalence for faithfully flat quantum homogeneous…
For a topological space $X$, we introduce a criterion for the $\rm FI$ module $H^i({\rm Conf}_n(X))$ to be finitely generated and give several applications. For instance, if $C$ is a finite connected $CW$ complex, then $X = C \times…
A finite element method for elliptic problems with discontinuous coefficients is presented. The discontinuity is assumed to take place along a closed smooth curve. The proposed method allows to deal with meshes that are not adapted to the…
A general theory for obtaining anisotropic interpolation error estimates for macro-element interpolation is developed revealing general construction principles. We apply this theory to interpolation operators on a macro type of biquadratic…
We consider families of reductive complexes related by level-raising operators and originating from an associative algebra. In the main theorem it is shown that the multiple cohomology of that complexes is given by the factor space of…
We study the mixed formulation of the abstract Hodge Laplacian on axisymmetric domains with general data through Fourer-finite-element-methods in weighted functions spaces. Closed Hilbert complexes and commuting projectors are used through…
The goal of this paper is to offer a new construction of the de Rham-Witt complex of smooth varieties over perfect fields of characteristic $p>0$. We introduce a category of cochain complexes equipped with an endomorphism $F$ of underlying…