8 citations · 11 across the 15 of their papers we have counts for
17 papers
Optimal Control in Hilbert Complex Spaces with Finite Element Exterior Calculus
Farid Bozorgnia, Michael Holst, Anshu Kumar +3
We develop a framework for PDE-constrained optimal control on Hilbert complexes and its structure-preserving discretization by finite element exterior calculus (FEEC), with emphasi…
Towards finite element exterior calculus on manifolds: commuting projections, geometric variational crimes, and approximation errors
Martin W. Licht
We survey recent contributions to finite element exterior calculus on manifolds and surfaces within a comprehensive formalism for the error analysis of vector-valued partial differ…
Smoothed projections over manifolds in finite element exterior calculus
Martin W. Licht
We develop commuting finite element projections on compact Riemannian smooth manifolds. The commuting projections are constructed using localized smoothing operators, building on a…
Higher-order finite element de Rham complexes, partially localized flux reconstructions, and applications
Martin Werner Licht
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 diffe…
Constructing collars in paracompact Hausdorff spaces and Lipschitz estimates
Martin Werner Licht
We give a constructive proof for the following new collar theorem: every locally collared closed set that is paracompact in a Hausdorff space is collared. This includes the importa…
Averaging-based local projections in finite element exterior calculus
Martin W. Licht
We construct local projection operators onto spaces of finite element differential forms on simplicial meshes. The projections are locally stable in Lebesgue and Sobolev--Slobodeck…
Finite Element Methods for Linear Maxwell's Equations in Bianisotropic Media Permitting Polarization Fields and Magnetic Currents
Tharindu Fernando, Martin Licht, Michael Holst
We review Maxwell's equations and constitutive relations for 3D bianisotropic media in a generalized form: we consider all four variables and allow for nonzero polarization or magn…
Higher-order chain rules for tensor fields, generalized Bell polynomials, and estimates in Orlicz-Sobolev-Slobodeckij and bounded variation spaces
Martin W. Licht
We describe higher-order chain rules for multivariate functions and tensor fields. We estimate Sobolev-Slobodeckij norms, Musielak-Orlicz norms, and the total variation seminorms o…
Local Finite Element Approximation of Sobolev Differential Forms
Evan S. Gawlik, Michael J. Holst, Martin W. Licht
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 th…
Symmetry and Invariant Bases in Finite Element Exterior Calculus
Martin W. Licht
We study symmetries of bases and spanning sets in finite element exterior calculus, using representation theory. We want to know which vector-valued finite element spaces have base…
A divergence-conforming finite element method for the surface Stokes equation
Andrea Bonito, Alan Demlow, Martin Licht
The Stokes equation posed on surfaces is important in some physical models, but its numerical solution poses several challenges not encountered in the corresponding Euclidean setti…
On Basis Constructions in Finite Element Exterior Calculus
Martin W. Licht
We give a systematic and self-contained account of the construction of geometrically decomposed bases and degrees of freedom in finite element exterior calculus. In particular, we…
Geometric Transformation of Finite Element Methods: Theory and Applications
M. Holst, M. Licht
We present a new technique to apply finite element methods to partial differential equations over curved domains. A change of variables along a coordinate transformation satisfying…
Smoothed Projections and Mixed Boundary Conditions
Martin W. Licht
Mixed boundary conditions are introduced to finite element exterior calculus. We construct smoothed projections from Sobolev de Rham complexes onto finite element de Rham complexes…
Flux Reconstruction for Goal-Oriented A Posteriori Error Estimation
Martin Licht, Matthias Maier
We propose a new heuristic goal-oriented a posteriori error estimator that connects the dual weighted residual method with equilibrated a posteriori error estimation. Our numerical…
Smoothed Projections over Weakly Lipschitz Domains
Martin Werner Licht
We develop finite element exterior calculus over weakly Lipschitz domains. Specifically, we construct commuting projections from de~Rham complexes over weakly Lipschitz domai…
Complexes of Discrete Distributional Differential Forms and their Homology Theory
Martin Werner Licht
Complexes of discrete distributional differential forms are introduced into finite element exterior calculus. Thus we generalize a notion of Braess and Schöberl, originally studied…