Error analysis of implicit and exponential time integration of linear Maxwell's equations

Pažur, Tomislav

doi:10.5445/ir/1000038617

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2022

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Cited by 2 publications

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“…The last result is another approximation property and generalizes Proposition 3.8 to more than one discrete operator. We point out that this result and its proof are generalizations of [35,Thm. 6.3].…”

Section: The Constants Are Given By Cmentioning

confidence: 54%

Error analysis of a fully discrete discontinuous Galerkin alternating direction implicit discretization of a class of linear wave-type problems

Hochbruck

Köhler

2022

Numer. Math.

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This paper is concerned with the rigorous error analysis of a fully discrete scheme obtained by using a central fluxes discontinuous Galerkin (dG) method in space and the Peaceman–Rachford splitting scheme in time. We apply the scheme to a general class of wave-type problems and show that the resulting approximations as well as discrete derivatives thereof satisfy error bounds of the order of the polynomial degree used in the dG discretization and order two in time. In particular, the class of problems considered includes, e.g., the advection equation, the acoustic wave equation, and the Maxwell equations for which a very efficient implementation is possible via an alternating direction implicit splitting.

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Section: The Constants Are Given By Cmentioning

confidence: 54%

Error analysis of a fully discrete discontinuous Galerkin alternating direction implicit discretization of a class of linear wave-type problems

Hochbruck

Köhler

2022

Numer. Math.

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Numerical Analysis of the Electro-Magnetic Perfectly Matched Layer in a Discontinuous Galerkin Discretization

Schulz¹

2015

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Error analysis of implicit and exponential time integration of linear Maxwell's equations

Cited by 2 publications

References 30 publications

Error analysis of a fully discrete discontinuous Galerkin alternating direction implicit discretization of a class of linear wave-type problems

Error analysis of a fully discrete discontinuous Galerkin alternating direction implicit discretization of a class of linear wave-type problems

Numerical Analysis of the Electro-Magnetic Perfectly Matched Layer in a Discontinuous Galerkin Discretization

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