Exact Non-reflecting Boundary Conditions Revisited: Well-Posedness and Stability

Sofia Eriksson; Jan Nordström

doi:10.1007/s10208-016-9310-3

Exact Non-reflecting Boundary Conditions Revisited: Well-Posedness and Stability

Sofia Eriksson, Jan Nordström

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

Abstract

Exact non-reflecting boundary conditions for a linear incompletely parabolic system in one dimension have been studied. The system is a model for the linearized compressible Navier–Stokes equations, but is less complicated which allows for a detailed analysis without approximations. It is shown that well-posedness is a fundamental property of the exact non-reflecting boundary conditions. By using summation by parts operators for the numerical approximation and a weak boundary implementation, it is also shown that energy stability follows automatically.

Original language	English
Pages (from-to)	957-986
Number of pages	30
Journal	Foundations of Computational Mathematics
Volume	17
Issue number	4
DOIs	https://doi.org/10.1007/s10208-016-9310-3
Publication status	Published - 1 Aug 2017
Externally published	Yes

Keywords

Non-reflecting boundary conditions
Stability
Summation by parts
Weak boundary implementation
Well-posedness

ASJC Scopus subject areas

Analysis
Computational Mathematics
Computational Theory and Mathematics
Applied Mathematics

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10.1007/s10208-016-9310-3

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abstract = "Exact non-reflecting boundary conditions for a linear incompletely parabolic system in one dimension have been studied. The system is a model for the linearized compressible Navier–Stokes equations, but is less complicated which allows for a detailed analysis without approximations. It is shown that well-posedness is a fundamental property of the exact non-reflecting boundary conditions. By using summation by parts operators for the numerical approximation and a weak boundary implementation, it is also shown that energy stability follows automatically.",

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AB - Exact non-reflecting boundary conditions for a linear incompletely parabolic system in one dimension have been studied. The system is a model for the linearized compressible Navier–Stokes equations, but is less complicated which allows for a detailed analysis without approximations. It is shown that well-posedness is a fundamental property of the exact non-reflecting boundary conditions. By using summation by parts operators for the numerical approximation and a weak boundary implementation, it is also shown that energy stability follows automatically.

KW - Non-reflecting boundary conditions

KW - Stability

KW - Summation by parts

KW - Weak boundary implementation

KW - Well-posedness

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Exact Non-reflecting Boundary Conditions Revisited: Well-Posedness and Stability

Abstract

Keywords

ASJC Scopus subject areas

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