Error analysis of splitting methods for wave type equations

Eilinghoff, Johannes

doi:10.5445/ir/1000075070

Cited by 1 publication

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“…Besides full discretization results, there exist several rigorous semidiscrete analyses for the Peaceman-Rachford scheme applied to the Maxwell equations interpreted as an abstract Cauchy problem. In [21], the homogeneous and in [6,8,9], the inhomogeneous and damped equations were considered. Further, in [44], a detailed analysis of the abstract Maxwell problem with jumping material parameters was performed, providing error bounds of order 3/2 for suitable data.…”

Section: Introductionmentioning

confidence: 99%

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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: Introductionmentioning

confidence: 99%

“…We point out that all these results pose assumptions only on the data, as opposed to the analysis carried out here, which assumes regularity of the exact solution. However, the regularity analysis carried out in [6,8,9,21] can be used to defer these assumptions to the data in the particular case of Maxwell equations.…”

Section: Introductionmentioning

confidence: 99%

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.

View full text Add to dashboard Cite

show abstract

Error analysis of splitting methods for wave type equations

Cited by 1 publication

References 0 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

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