dc.date.accessioned | 2024-03-02T16:48:34Z | |
dc.date.available | 2024-03-02T16:48:34Z | |
dc.date.created | 2023-03-29T21:30:32Z | |
dc.date.issued | 2023 | |
dc.identifier.citation | Christiansen, Snorre H Halvorsen, Tore Gunnar Scheid, Claire . Convergence of a discretization of the Maxwell–Klein–Gordon equation based on finite element methods and lattice gauge theory. Numerical Methods for Partial Differential Equations. 2023 | |
dc.identifier.uri | http://hdl.handle.net/10852/108932 | |
dc.description.abstract | Abstract 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 a particle. The solutions, expressed with a magnetic vector potential, are invariant under gauge transformations. This characteristic implies a constraint on the solution fields that might be broken at the discrete level. In this article, we propose and study a constraint preserving numerical scheme for this set of equations in dimension 2. At the semidiscrete level, we combine conforming Finite Element discretizations with the so‐called Lattice Gauge Theory to design a compatible gauge invariant discretization, leading to preservation of a discrete constraint. Relying on energy techniques and compactness arguments, we establish the convergence of this semidiscrete scheme, without a priori knowledge of the solution. Finally, at the fully discrete level, we propose a compatible explicit time‐integration strategy of leapfrog type. We implement the resulting fully discrete scheme and provide assessment on academic scenarios. | |
dc.language | EN | |
dc.publisher | Wiley-Interscience Publishers | |
dc.rights | Attribution 4.0 International | |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
dc.title | Convergence of a discretization of the Maxwell–Klein–Gordon equation based on finite element methods and lattice gauge theory | |
dc.title.alternative | ENEngelskEnglishConvergence of a discretization of the Maxwell–Klein–Gordon equation based on finite element methods and lattice gauge theory | |
dc.type | Journal article | |
dc.creator.author | Christiansen, Snorre H | |
dc.creator.author | Halvorsen, Tore Gunnar | |
dc.creator.author | Scheid, Claire | |
cristin.unitcode | 185,15,13,45 | |
cristin.unitname | Differensiallikninger og beregningsorientert matematikk | |
cristin.ispublished | true | |
cristin.fulltext | postprint | |
cristin.qualitycode | 1 | |
dc.identifier.cristin | 2138306 | |
dc.identifier.bibliographiccitation | info:ofi/fmt:kev:mtx:ctx&ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Numerical Methods for Partial Differential Equations&rft.volume=&rft.spage=&rft.date=2023 | |
dc.identifier.jtitle | Numerical Methods for Partial Differential Equations | |
dc.identifier.volume | 39 | |
dc.identifier.issue | 4 | |
dc.identifier.startpage | 3271 | |
dc.identifier.endpage | 3308 | |
dc.identifier.pagecount | 0 | |
dc.identifier.doi | https://doi.org/10.1002/num.23008 | |
dc.type.document | Tidsskriftartikkel | |
dc.type.peerreviewed | Peer reviewed | |
dc.source.issn | 0749-159X | |
dc.type.version | PublishedVersion | |