Search Results - "Christiansen, Snorre H."

A dual finite element complex on the barycentric refinement by Buffa, Annalisa, Christiansen, Snorre H.

“…Given a two dimensional oriented surface equipped with a simplicial mesh, the standard lowest order finite element spaces provide a complex X^\bullet centered…”
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On high order finite element spaces of differential forms by Christiansen, Snorre H., Rapetti, Francesca

“…We show how the high order finite element spaces of differential forms due to Raviart-Thomas-Nédelec-Hiptmair fit into the framework of finite element systems,…”
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On eigenmode approximation for Dirac equations: Differential forms and fractional Sobolev spaces by CHRISTIANSEN, SNORRE H.

“…We comment on the discretization of the Dirac equation using finite element spaces of differential forms. In order to treat perturbations by low order terms,…”
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Smoothed projections in finite element exterior calculus by Christiansen, Snorre H., Winther, Ragnar

“…The development of smoothed projections, constructed by combining the canonical interpolation operators defined from the degrees of freedom with a smoothing…”
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Generalized finite element systems for smooth differential forms and Stokes’ problem by Christiansen, Snorre H., Hu, Kaibo

“…We provide both a general framework for discretizing de Rham sequences of differential forms of high regularity, and some examples of finite element spaces…”
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On the definition of curvature in Regge calculus by Christiansen, Snorre H

“…Regge calculus defines a curvature for piecewise constant metrics on simplicial complexes subject to a partial continuity requirement. We prove that if a part…”
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Nodal finite element de Rham complexes by Christiansen, Snorre H., Hu, Jun, Hu, Kaibo

“…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…”
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Finite Element Systems for Vector Bundles: Elasticity and Curvature by Christiansen, Snorre H., Hu, Kaibo

“…We develop a theory of finite element systems, for the purpose of discretizing sections of vector bundles, in particular those arising in the theory of…”
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A discrete elasticity complex on three-dimensional Alfeld splits by Christiansen, Snorre H., Gopalakrishnan, Jay, Guzmán, Johnny, Hu, Kaibo

“…We construct conforming finite element elasticity complexes on the Alfeld splits of tetrahedra. The complex consists of vector fields and symmetric tensor…”
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Application of a minimal compatible element to incompressible and nearly incompressible continuum mechanics by Burman, Erik, Christiansen, Snorre H., Hansbo, Peter

“…In this note we will explore some applications of the recently constructed piecewise affine, H1-conforming element that fits in a discrete de Rham complex…”
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A Preconditioner for the Electric Field Integral Equation Based on Calderon Formulas by Christiansen, Snorre H., Nédélec, Jean-Claude

“…We describe a preconditioning technique for the Galerkin approximation of the electric field integral equation (EFIE), which arises in the scattering theory…”
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On the linearization of Regge calculus by Christiansen, Snorre H.

“…We study the linearization of three dimensional Regge calculus around Euclidean metric. We provide an explicit formula for the corresponding quadratic form and…”
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Discrete Fredholm properties and convergence estimates for the electric field integral equation by CHRISTIANSEN, Snorre H

“…The Galerkin discretization of the Electric Field Integral Equation is reinvestigated. We prove quasi-optimal convergence estimates at nonresonant frequencies,…”
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Convergence of a discretization of the Maxwell–Klein–Gordon equation based on finite element methods and lattice gauge theory by Christiansen, Snorre H., Halvorsen, Tore G., Scheid, Claire

“…The Maxwell–Klein–Gordon equations are a set of coupled nonlinear time‐dependent wave equations, used to model the interaction of an electromagnetic field with…”
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Poincaré–Friedrichs inequalities of complexes of discrete distributional differential forms by Christiansen, Snorre H., Licht, Martin W.

“…We derive bounds for the constants in Poincaré–Friedrichs inequalities with respect to mesh-dependent norms for complexes of discrete distributional…”
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Stability of hodge decompositions in finite element spaces of differential forms in arbitrary dimension by CHRISTIANSEN, Snorre H

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On variational eigenvalue approximation of semidefinite operators by Christiansen, S. H., Winther, R.

“…Eigenvalue problems for semidefinite operators with infinite-dimensional kernels appear, for instance, in electromagnetics. Variational discretizations with…”
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A GAUGE INVARIANT DISCRETIZATION ON SIMPLICIAL GRIDS OF THE SCHRÖDINGER EIGENVALUE PROBLEM IN AN ELECTROMAGNETIC FIELD by CHRISTIANSEN, SNORRE H., HALVORSEN, TORE G.

“…We propose a method to compute approximate eigenpairs of the Schrödinger operator on a bounded domain in the presence of an electromagnetic field. Formulated…”
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Discretizing the Maxwell-Klein-Gordon equation by the lattice gauge theory formalism by CHRISTIANSEN, Snorre H, HALVORSEN, Tore Gunnar

“…In this article we study the discretization of the Maxwell-Klein-Gordon equation from a variational point of view. We first solve the problem with an action…”
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Convergence of lattice gauge theory for Maxwell’s equations by Christiansen, Snorre H., Halvorsen, Tore Gunnar

“…In this article we prove convergence of Lattice Gauge Theory in the energy norm for electromagnetism, which corresponds to gauge group U(1). This is done by…”
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