The metric tensor of a Riemannian manifold can be approximated using Regge finite
elements and such approximations can be used to compute approximations to the Gauss …

Regge calculus defines a curvature for piecewise constant metrics on simplicial complexes
subject to a partial continuity requirement. We prove that if a part of the complex is …

We present a finite element technique for approximating the surface Hessian of a discrete
scalar function on triangulated surfaces embedded in, with or without boundary. We then …

We analyze finite element discretizations of scalar curvature in dimension $ N\ge 2$. Our
analysis focuses on piecewise polynomial interpolants of a smooth Riemannian metric $ g …

We construct finite element approximations of the Levi-Civita connection and its curvature on
triangulations of oriented two-dimensional manifolds. Our construction relies on the Regge …

This paper uses the technology of weighted triangulations to study discrete versions of the
Laplacian on piecewise Euclidean manifolds. Given a collection of Euclidean simplices …

We construct and analyze finite element approximations of the Einstein tensor in dimension
$ N\ge 3$. We focus on the setting where a smooth Riemannian metric tensor $ g $ on a …

In this paper we propose a definition of the distributional Riemann curvature tensor in
dimension $ N\geq 2$ if the underlying metric tensor $ g $ defined on a triangulation …

In this paper we propose a generalization of the Riemann curvature tensor on manifolds (of
dimension two or higher) endowed with a Regge metric. Specifically, while all components …

We study the diffusion of tangential tensor-valued data on curved surfaces. For this purpose,
several finite-element-based numerical methods are collected and used to solve a …