Well-posedness, stability and conservation for a discontinuous interface problem

Cristina La Cognata; Jan Nordström

doi:10.1007/s10543-015-0576-7

Well-posedness, stability and conservation for a discontinuous interface problem

Cristina La Cognata, Jan Nordström

Linköping University

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

4 Citations (Scopus)

Abstract

The advection equation is studied in a completely general two domain setting with different wave-speeds and a time-independent jump-condition at the interface separating the domains. Well-posedness and conservation criteria are derived for the initial-boundary-value problem. The equations are semi-discretized using a finite difference method on Summation-By-Part (SBP) form. The relation between the stability and conservation properties of the approximation are studied when the boundary and interface conditions are weakly imposed by the Simultaneous-Approximation-Term (SAT) procedure. Numerical simulations corroborate the theoretical findings.

Original language	English
Pages (from-to)	681-704
Number of pages	24
Journal	BIT Numerical Mathematics
Volume	56
Issue number	2
DOIs	https://doi.org/10.1007/s10543-015-0576-7
Publication status	Published - 1 Jun 2016
Externally published	Yes

Keywords

Conservation
Discontinuous coefficients problems
High order accuracy
Initial boundary value problems
Interface
Interface conditions
Stability
Summation-by-parts operators
Well-posedness

ASJC Scopus subject areas

Software
Computer Networks and Communications
Computational Mathematics
Applied Mathematics

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10.1007/s10543-015-0576-7

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title = "Well-posedness, stability and conservation for a discontinuous interface problem",

abstract = "The advection equation is studied in a completely general two domain setting with different wave-speeds and a time-independent jump-condition at the interface separating the domains. Well-posedness and conservation criteria are derived for the initial-boundary-value problem. The equations are semi-discretized using a finite difference method on Summation-By-Part (SBP) form. The relation between the stability and conservation properties of the approximation are studied when the boundary and interface conditions are weakly imposed by the Simultaneous-Approximation-Term (SAT) procedure. Numerical simulations corroborate the theoretical findings.",

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AU - La Cognata, Cristina

AU - Nordström, Jan

PY - 2016/6/1

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N2 - The advection equation is studied in a completely general two domain setting with different wave-speeds and a time-independent jump-condition at the interface separating the domains. Well-posedness and conservation criteria are derived for the initial-boundary-value problem. The equations are semi-discretized using a finite difference method on Summation-By-Part (SBP) form. The relation between the stability and conservation properties of the approximation are studied when the boundary and interface conditions are weakly imposed by the Simultaneous-Approximation-Term (SAT) procedure. Numerical simulations corroborate the theoretical findings.

AB - The advection equation is studied in a completely general two domain setting with different wave-speeds and a time-independent jump-condition at the interface separating the domains. Well-posedness and conservation criteria are derived for the initial-boundary-value problem. The equations are semi-discretized using a finite difference method on Summation-By-Part (SBP) form. The relation between the stability and conservation properties of the approximation are studied when the boundary and interface conditions are weakly imposed by the Simultaneous-Approximation-Term (SAT) procedure. Numerical simulations corroborate the theoretical findings.

KW - Conservation

KW - Discontinuous coefficients problems

KW - High order accuracy

KW - Initial boundary value problems

KW - Interface

KW - Interface conditions

KW - Stability

KW - Summation-by-parts operators

KW - Well-posedness

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JO - BIT Numerical Mathematics

JF - BIT Numerical Mathematics

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Well-posedness, stability and conservation for a discontinuous interface problem

Abstract

Keywords

ASJC Scopus subject areas

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