Browsing Matematisk institutt by Author "Christiansen, Snorre H."
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Christiansen, Snorre H. (Research report / Forskningsrapport, 2003)We describe all operators on scalar finite element spaces which appear as the restriction of a second order (linear) differential operator. More precisely we provide a family of isomorphisms between this space of discrete ...

Christiansen, Snorre H. (Research report / Forskningsrapport, 2007)We study discretizations of the MaxwellKleinGordon equation as an example of a constrained geometric nonlinear evolution partial differential equation. For the temporal gauge we propose a fully discrete scheme which ...

Scheid, Claire; Christiansen, Snorre H. (Research report / Forskningsrapport, 2009)As an example of a simple constrained geometric nonlinear wave equation, we study a numerical approximation of the Maxwell Klein Gordon equation. We consider an existing constraint preserving semidiscrete scheme based ...

Christiansen, Snorre H.; Halvorsen, Tore Gunnar (Research report / Forskningsrapport, 2008)In this article we show convergence of Lattice Gauge Theory with gauge group U(1) in the energy norm. This is done by stability analysis and comparison with the classical Yeescheme which is convergent.

Christiansen, Snorre H. (Research report / Forskningsrapport, 2003)A variant of Murat and Tartar's divcurl lemma is stated and proved for Nédélec's edge elements. For sequences of vector fields in sequences of such finite element spaces the hypothesis on the divergence can be put into a ...

Christiansen, Snorre H. (Research report / Forskningsrapport, 2009)Étant donné un complexe cellulaire constitué de polyèdres, plongé dans un espace Euclidien, nous construisons des espaces d'éléments finis de formes différentielles contenant celles qui sont polynomiales de degré maximal ...

Christiansen, Snorre H. (Research report / Forskningsrapport, 2009)The first part of the paper is an overview of the theory of approximation of wave equations by Galerkin methods. It treats convergence theory for linear second order evolution equations and includes studies of consistency ...

Christiansen, Snorre H.; Halvorsen, Tore Gunnar (Research report / Forskningsrapport, 2009)We propose a method to compute approximate eigenpairs of the Schrödinger operator on a bounded domain in the presence of an electromagnetic field. The method is formulated for the simplicial grids that satisfy the discrete ...

Christiansen, Snorre H.; Winther, Ragnar (Research report / Forskningsrapport, 2004)The problem of constraint preservation for discretizations of nonlinear PDEs is addressed on the example of the hyperbolic YangMills equations in temporal gauge. These equations preserve a nonlinear divergence field ...

Christiansen, Snorre H. (Research report / Forskningsrapport, 2009)

Christiansen, Snorre H. (Research report / Forskningsrapport, 2008)We study the linearization of three dimensional Regge calculus around Euclidean metric. We provide an explicit formula for the corresponding quadratic form and relate it to the curl T curl operator which appears in the ...

Christiansen, Snorre H.; Winther, Ragnar (Research report / Forskningsrapport, 2006)The development of smoothed projections, constructed by combining the canonical interpolation operators defined from the degrees of freedom with a smoothing operator, have proved to be an effective tool in finite element ...

Christiansen, Snorre H.; Halvorsen, Tore Gunnar (Research report / Forskningsrapport, 2008)In this article we study the discretization of the MaxwellKleinGordon equation from a variational point of view. We first solve the problem with an action corresponding to the Yee scheme for the Maxwell part, which is ...

Christiansen, Snorre H. (Research report / Forskningsrapport, 2005)We elaborate on the interpretation of some mixed finite element spaces in terms of differential forms. First we develop a framework in which we show how tools from algebraic topology can be applied to the study of their ...

Christiansen, Snorre H. (Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2013)We provide a notion of finite element system, that enables the construction spaces of differential forms, which can be used for the numerical solution of variationally posed partial difeerential equations. Within this ...