Finite element de Rham and Stokes complexes in three dimensions

Differential Complexes and Stability of Finite Element Methods. I. the De Rham Complex

In this paper we explain the relation between certain piecewise polynomial subcomplexes of the de Rham complex and the stability of mixed finite element methods for elliptic problems.

Finite Element Mesh Optimization in Three Dimensions

We discuss an optimization procedure for improving three-dimensional finite element meshes. Our method can be effectively coupled with any automatic mesh generator in order to obtain a triangulation without badly distorted elements. In this way, we are able to weaken the requirements on the generator, allowing it to produce singular elements, and post-process the result to get a valid mesh. Eve...

Rigid Cohomology and De Rham-witt Complexes

Let k be a perfect field of characteristic p > 0, Wn = Wn(k). For separated k-schemes of finite type, we explain how rigid cohomology with compact supports can be computed as the cohomology of certain de Rham-Witt complexes with coefficients. This result generalizes the classical comparison theorem of Bloch-Illusie for proper and smooth schemes. In the proof, the key step is an extension of the...

On Higher Order Finite Element Discretizations for the Incompressible Navier-stokes Equations in Three Dimensions

Analytic Torsion for Twisted De Rham Complexes

We define analytic torsion τ (X,E ,H) ∈ detH(X, E ,H) for the twisted de Rham complex, consisting of differential forms on a compact Riemannian manifold X valued in a flat vector bundle E , with a differential given by ∇ +H ∧ · , where ∇ is a flat connection on E , H is an odd-degree closed differential form on X, and H(X, E ,H) denotes the cohomology of this Z2-graded complex. We show that whe...