Convergence of a discretization of the Maxwell-Klein-Gordon equation based on Finite Element Methods and Lattice Gauge Theory - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Numerical Methods for Partial Differential Equations Year : 2023

Convergence of a discretization of the Maxwell-Klein-Gordon equation based on Finite Element Methods and Lattice Gauge Theory

Abstract

In this article we study a semi-discrete numerical scheme for the Maxwell-Klein-Gordon equation in two spatial dimensions, based on Finite Elements and Lattice Gauge Theory (LGT). The discretization procedure from LGT, together with a numerical quadrature, ensures gauge invariance of the scheme. The gauge invariance implies that the scheme is constraint preserving. We combine this with energy conservation to prove convergence of the scheme towards a weak solution, for initial data of finite energy. Finally, we propose and implement a numerical scheme to assess our results.
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Dates and versions

hal-03513047 , version 1 (05-01-2022)
hal-03513047 , version 2 (08-02-2024)

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Snorre Christiansen, Tore G Halvorsen, Claire Scheid. 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, 39 (4), pp.3271-3308. ⟨10.1002/num.23008⟩. ⟨hal-03513047v2⟩
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