Related papers: A systematic construction of finite element commut…
We present new finite elements for solving the Riesz maps of the de Rham complex on triangular and tetrahedral meshes at high order. The finite elements discretize the same spaces as usual, but with different basis functions, so that the…
We investigate the mutual relations between the centers of different elements in the deconstruction lattice of a 2D conformal model, and show how these can be described using exact sequences of abelian groups. In particular, we exhibit a…
We introduce a forcing technique to construct three-dimensional arrays of generic extensions through FS (finite support) iterations of ccc posets, which we refer to as 3D-coherent systems. We use them to produce models of new constellations…
In this paper, we propose two families of nonconforming finite elements on $n$-rectangle meshes of any dimension to solve the sixth-order elliptic equations. The unisolvent property and the approximation ability of the new finite element…
We construct several smooth finite element spaces defined on three--dimensional Worsey--Farin splits. In particular, we construct $C^1$, $H^1(\curl)$, and $H^1$-conforming finite element spaces and show the discrete spaces satisfy local…
A finite element cochain complex on Cartesian meshes of any dimension based on the H1-inner product is introduced. It yields H1-conforming finite element spaces with exterior derivatives in H1. We use a tensor product construction to obtain…
We develop a method to compute $H^2$-conforming finite element approximations in both two and three space dimensions using readily available finite element spaces. This is accomplished by deriving a novel, equivalent mixed variational…
We present a family of high-order finite element approximation spaces on a pyramid, and associated unisolvent degrees of freedom. These spaces consist of rational basis functions. We establish conforming, exactness and polynomial…
In work the internal structure of de Rham cohomology is considered. As examples the phase flows in $\mathbb {R}^3$ admitting the Nambu Poisson structure are studied.
This article surveys research on the application of compatible finite element methods to large scale atmosphere and ocean simulation. Compatible finite element methods extend Arakawa's C-grid finite difference scheme to the finite element…
We construct 2D and 3D finite element de Rham sequences of arbitrary polynomial degrees with extra smoothness. Some of these elements have nodal degrees of freedom (DoFs) and can be considered as generalisations of scalar Hermite and…
In this paper, the first family of conforming discrete three dimensional Gradgrad-complexes consisting of finite element spaces is constructed. These discrete complexes are exact in the sense that the range of each discrete map is the…
This paper presents a novel exact finite element formulation of quasi-3D beam for high-fidelity analysis of functionally graded sandwich beams. Unlike conventional displacement-based elements that rely on approximate interpolation functions…
We create a framework for studying symmetric chain decompositions of families of finite posets based on the geometry of polytopes. Our framework unifies almost all known results regarding symmetric chain decompositions of the Young posets…
We construct smooth finite elements spaces on Powell-Sabin triangulations that form an exact sequence. The first space of the sequence coincides with the classical $C^1$ Powell-Sabin space, while the others form stable and divergence-free…
We construct finite element de~Rham complexes of higher and possibly non-uniform polynomial order in finite element exterior calculus (FEEC). Starting from the finite element differential complex of lowest-order, known as the complex of…
An explicit construction of infinite sequences of strongly regular digraphs with parameter sets $((v+(2^{n+1}-4)t)2^{n-1}, k+(2^n-2)t, t, \lambda, t)$ is described. A computer program was used to find the initial digraphs. The remaining…
Two types of finite element spaces on triangles are constructed for div-div conforming symmetric tensors. Besides the normal-normal continuity, the stress tensor is continuous at vertices and another trace involving combination of…
In the field of solving partial differential equations (PDEs), Hilbert complexes have become highly significant. Recent advances focus on creating new complexes using the Bernstein-Gelfand-Gelfand (BGG) framework, as shown by Arnold and Hu…
We consider a notion of exact sequences in any -not necessarily exact- pointed category relative to a given (E;M)-factorization structure. We apply this notion to introduce and investigate a new notion of exact sequences of semimodules over…