Robust boundary conditions for stochastic incompletely parabolic systems of equations

Markus Wahlsten; Jan Nordström

doi:10.1016/j.jcp.2018.04.060

Robust boundary conditions for stochastic incompletely parabolic systems of equations

Markus Wahlsten, Jan Nordström

Linköping University

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

1 Citation (Scopus)

Abstract

We study an incompletely parabolic system in three space dimensions with stochastic boundary and initial data. We show how the variance of the solution can be manipulated by the boundary conditions, while keeping the mean value of the solution unaffected. Estimates of the variance of the solution is presented both analytically and numerically. We exemplify the technique by applying it to an incompletely parabolic model problem, as well as the one-dimensional compressible Navier–Stokes equations.

Original language	English
Pages (from-to)	192-213
Number of pages	22
Journal	Journal of Computational Physics
Volume	371
DOIs	https://doi.org/10.1016/j.jcp.2018.04.060
Publication status	Published - 15 Oct 2018
Externally published	Yes

Keywords

Incompletely parabolic system
Initial boundary value problems
Robust design
Stochastic data
Uncertainty quantification
Variance reduction

ASJC Scopus subject areas

Numerical Analysis
Modeling and Simulation
Physics and Astronomy (miscellaneous)
General Physics and Astronomy
Computer Science Applications
Computational Mathematics
Applied Mathematics

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10.1016/j.jcp.2018.04.060

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title = "Robust boundary conditions for stochastic incompletely parabolic systems of equations",

abstract = "We study an incompletely parabolic system in three space dimensions with stochastic boundary and initial data. We show how the variance of the solution can be manipulated by the boundary conditions, while keeping the mean value of the solution unaffected. Estimates of the variance of the solution is presented both analytically and numerically. We exemplify the technique by applying it to an incompletely parabolic model problem, as well as the one-dimensional compressible Navier–Stokes equations.",

keywords = "Incompletely parabolic system, Initial boundary value problems, Robust design, Stochastic data, Uncertainty quantification, Variance reduction",

author = "Markus Wahlsten and Jan Nordstr{\"o}m",

note = "Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",

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AU - Nordström, Jan

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N2 - We study an incompletely parabolic system in three space dimensions with stochastic boundary and initial data. We show how the variance of the solution can be manipulated by the boundary conditions, while keeping the mean value of the solution unaffected. Estimates of the variance of the solution is presented both analytically and numerically. We exemplify the technique by applying it to an incompletely parabolic model problem, as well as the one-dimensional compressible Navier–Stokes equations.

AB - We study an incompletely parabolic system in three space dimensions with stochastic boundary and initial data. We show how the variance of the solution can be manipulated by the boundary conditions, while keeping the mean value of the solution unaffected. Estimates of the variance of the solution is presented both analytically and numerically. We exemplify the technique by applying it to an incompletely parabolic model problem, as well as the one-dimensional compressible Navier–Stokes equations.

KW - Incompletely parabolic system

KW - Initial boundary value problems

KW - Robust design

KW - Stochastic data

KW - Uncertainty quantification

KW - Variance reduction

UR - http://www.scopus.com/inward/record.url?scp=85047811384&partnerID=8YFLogxK

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DO - 10.1016/j.jcp.2018.04.060

M3 - Article

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SN - 0021-9991

VL - 371

SP - 192

EP - 213

JO - Journal of Computational Physics

JF - Journal of Computational Physics

ER -

Robust boundary conditions for stochastic incompletely parabolic systems of equations

Abstract

Keywords

ASJC Scopus subject areas

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