Snorre Harald Christiansen

Image of Snorre Harald Christiansen
Norwegian version of this page
Phone +47 22857774
Room 1013
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Visiting address Moltke Moes vei 35 Niels Henrik Abels hus 0851 Oslo
Postal address Postboks 1053 Blindern 0316 Oslo

I work on numerical analysis for partial differential equations. I am particularly interested in developing and studying finite element methods for electromagnetics and continuum mechanics and more generally the de Rham complex. I introduced dual finite element complexes and Calderon preconditioners for the boundary element method in electromagnetics. I have related methods from theoretical physics, especially Regge calculus (developed for general relativity) and lattice gauge theory (developed for quantum chromodynamics), to finite element methods, thereby allowing for a new numerical analysis. I have introduced a framework called finite element systems to design new spaces for fluid flow (the Stokes equation) and geometry (the elasticity complex).

Research statement and publication list

More information at the Norwegian page.

 

Tags: Mathematics, Partial Differential Equations, numerical analysis

Publications

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  • Christiansen, Snorre H (2016). Uniformly stable finite elements for convection diffusion equations.
  • Christiansen, Snorre H (2016). On curvature of piecewise flat manifolds.
  • Christiansen, Snorre H (2013). Dual finite elements for Calderon preconditioning of the Electric Field Integral Equation.
  • Christiansen, Snorre H (2013). Systèmes d’éléments finis de formes différentielles, variantes sous le vent.
  • Christiansen, Snorre H (2013). Constraint preservation in Lattice Gauge Theory.
  • Christiansen, Snorre H (2013). Finite element systems of differential forms.
  • Christiansen, Snorre H (2013). Finite element systems of differential forms and applications to upwinding.
  • Christiansen, Snorre H (2011). Giovani matematici crescono: Snorre Christiansen. [Internet]. http://maddmaths.simai.eu/giovani-matematici-crescono/snorre.
  • Christiansen, Snorre H (2011). Upwinding in finite element spaces of differential forms.
  • Christiansen, Snorre H (2011). Spectral correctness of linearized Regge calculus.
  • Christiansen, Snorre H (2010). Introduction to Regge calculus and its linearization.
  • Christiansen, Snorre H (2010). Introduction to mixed finite elements.
  • Christiansen, Snorre H (2010). Lattice gauge theory meets finite elements.
  • Christiansen, Snorre H (2010). Éléments finis mixtes minimaux sur les polyèdres.
  • Christiansen, Snorre H (2010). Éléments finis mixtes minimaux sur les polyèdres.
  • Christiansen, Snorre H (2010). On the linearization of Regge Calculus in 3D.
  • Christiansen, Snorre H (2010). Coupling Maxwell with Schrödinger equations using Lattice Gauge Theory.
  • Christiansen, Snorre H (2010). Mixed finite elements as inverse systems of differential forms.
  • Christiansen, Snorre H (2010). Gauge invariant discretizations of Schrödinger equations in an electromagnetic field.
  • Christiansen, Snorre H (2010). Applications of lattice gauge theory to the coupling of Maxwell with Klein-Gordon and Schroedinger equations.
  • Christiansen, Snorre H (2010). A construction of minimal finite element spaces of differential forms on polyhedra.
  • Christiansen, Snorre H (2009). A framework for the discretization of differential forms on cellular complexes.
  • Christiansen, Snorre H (2009). Discretizing the Yang-Mills-Higgs equation.
  • Christiansen, Snorre H (2009). Finite elements and differential forms.
  • Christiansen, Snorre H (2009). Finite element exterior calculus on cellular complexes.
  • Christiansen, Snorre H (2009). A discussion of the div-curl lemma in a Galerkin setting.
  • Christiansen, Snorre H (2009). On the div-curl lemma in a Galerkin setting.
  • Christiansen, Snorre H (2008). On the linearization of Regge calculus.
  • Christiansen, Snorre H (2008). Discrete differential forms: from algebraic topology to approximation of Maxwell's equations.
  • Christiansen, Snorre H (2008). Regge calculus as a non-standard finite element method.
  • Christiansen, Snorre H (2008). A construction of spaces of compatible differential forms on cellular complexes.
  • Christiansen, Snorre H (2008). A construction of spaces of mixed finite elements on cellular complexes.
  • Christiansen, Snorre H (2007). Discrete differential forms: from algebraic topology to approximation of Maxwell's equations.
  • Christiansen, Snorre H (2007). Constraint preserving discretizations for some gauge invariant wave equations.
  • Christiansen, Snorre H (2007). A construction of mixed finite element spaces on polyhedral meshes.
  • Christiansen, Snorre H (2007). Constraint preserving schemes for some gauge invariant wave equations.
  • Christiansen, Snorre H (2006). Skolen ble en døråpner. [Newspaper]. Dagbladet.
  • Christiansen, Snorre H (2006). A construction of mixed finite element spaces on polyhedral meshes.
  • Christiansen, Snorre H (2006). Some homological algebra techniques in numerical analysis.
  • Christiansen, Snorre H (2006). On constraint preservation in numerical simulations of Yang-Mills equations.
  • Christiansen, Snorre H (2005). On divergence control in numerical simulations of Yang-Mills equations.
  • Christiansen, Snorre H & Buffa, Annalisa (2005). A dual finite element complex on the barycentric refinement.
  • Christiansen, Snorre H (2005). On constraint preservation in finite element discretizations of Yang-Mills equations.
  • Christiansen, Snorre H (2005). On constraint preservation in numerical simulations of Yang-Mills equations.
  • Christiansen, Snorre H (2005). On constraint preservation in numerical simulations of Yang-Mills equations.
  • Christiansen, Snorre H (2005). On numerical simulation of Yang-Mills equations.
  • Christiansen, Snorre H (2004). Constraint preservation and gauge invariance in discretizations of Maxwell and Yang-Mills equations.
  • Christiansen, Snorre H (2004). Numerical simulation of a non-linearly constrained evolution PDE: the Yang-Mills equations.
  • Christiansen, Snorre H (2004). Sur le controle de la divergence dans la simulation numerique des equations de Yang-Mills.
  • Christiansen, Snorre H (2004). On divergence control in numerical simulations of Yang-Mills equations.
  • Christiansen, Snorre H (2004). Two talks on preconditioning the Electric Field Integral Equation.
  • Christiansen, Snorre H (2004). A compensated compactness property of some finite element spaces.
  • Christiansen, Snorre H (2004). Sobre la simulacion numerica de las ecuaciones de Yang-Mills.
  • Christiansen, Snorre H (2004). On divergence control in numerical simulations of Yang-Mills equations.
  • Christiansen, Snorre H (2010). On variational eigenvalue approximation of semidefinite operators. ArXiv.
  • Christiansen, Snorre H & Halvorsen, Tore Gunnar (2010). A simplicial gauge theory. http://arxiv.org/abs/1006.2059v3.
  • Christiansen, Snorre H & Scheid, Claire (2009). Convergence of a constrained finite element discretization of the Maxwell Klein Gordon equation. Matematisk Institutt, Universitetet i Oslo. ISSN 0806-2439.
  • Christiansen, Snorre H (2009). Éléments finis mixtes minimaux sur les polyèdres. Matematisk Institutt, Universitetet i Oslo. ISSN 0806-2439.
  • Christiansen, Snorre H & Halvorsen, Tore Gunnar (2009). A gauge invariant discretization on simplicial grids of the Schrödinger eigenvalue problem in a magnetic field. Matematisk Institutt, Universitetet i Oslo. ISSN 0806-2439.
  • Halvorsen, Tore Gunnar; Christiansen, Snorre H & Winther, Ragnar (2009). Structure preserving discretizations of wave equations from theoretical physics. Unipub AS.
  • Christiansen, Snorre H & Halvorsen, Tore Gunnar (2008). Solving the Maxwell-Klein-Gordon equation in the Lattice Gauge Theory formalism. University of Oslo, Department of Mathematics.
  • Christiansen, Snorre H & Halvorsen, Tore Gunnar (2008). Convergence of lattice gauge theory for Maxwell's equations. University of Oslo, Department of Mathematics.
  • Christiansen, Snorre H (2008). On the linearization of Regge calculus. University of Oslo, Department of Mathematics.
  • Christiansen, Snorre H (2007). Constraint preserving schemes for some gauge invariant wave equations. Matematisk Institutt, Universitetet i Oslo. ISSN 0806-2439.
  • Christiansen, Snorre H & Winther, Ragnar (2006). Smoothed projections in finite element exterior calculus. Department of Mathematics.
  • Buffa, Annalisa & Christiansen, Snorre H (2005). A dual finite element complex on the barycentric refinement. IMATI-CNR.
  • Christiansen, Snorre H (2005). Stability of Hodge decompositions in finite element spaces of differential forms in arbitrary dimension. Matematisk Institutt.
  • Christiansen, Snorre H (2005). A construction of spaces of differential forms on cellular complexes. Institut Mittag-Leffler.
  • Christiansen, Snorre H & Winther, Ragnar (2004). On constraint preservation in numerical simulations of Yang-Mills equations. Matematisk Institutt, Universitetet i Oslo.

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Published Nov. 30, 2010 11:20 PM - Last modified Sep. 29, 2022 1:48 PM

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