For a piecewise polynomial finite element space 시 1 p, ΓD (𝒯)⊂ HΓD (curl, Ω) builton a
mesh 𝒯 ofa Lipschitzdomain Ω⊂ ℝ3 andwith vanishingtangentialtraceon ΓD⊂𝜕 Ω, a …

We address fundamental aspects in the approximation theory of vector-valued finite element
methods, using finite element exterior calculus as a unifying framework. We generalize the …

We develop projection operators onto finite element differential forms over simplicial
meshes. Our projection is locally bounded in Lebesgue and Sobolev-Slobodeckij norms …

We derive bounds for the constants in Poincaré–Friedrichs inequalities with respect to mesh-
dependent norms for complexes of discrete distributional differential forms. A key tool is a …

Boundary value problems for the Euclidean Hodge‐Laplacian in three dimensions− Δ HL:=
curl curl− grad div lead to variational formulations set in subspaces of H (curl, Ω)∩ H (div …

We present a new analysis of finite element methods for partial differential equations over
curved domains. In many applications, a change of variables translates a physical Poisson …

The problem of solving partial differential equations (PDEs) on manifolds can be considered
to be one of the most general problem formulations encountered in computational multi …