Error estimation and adaptive moment hierarchies for goal-oriented approximations of the Boltzmann equation

M.R.A. Abdelmalik; E.H. van Brummelen

doi:10.1016/j.cma.2017.06.024

Error estimation and adaptive moment hierarchies for goal-oriented approximations of the Boltzmann equation

M.R.A. Abdelmalik, E.H. van Brummelen

Energy Technology

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8 Citations (Scopus)

Abstract

This paper presents an a-posteriori goal-oriented error analysis for a numerical approximation of the steady Boltzmann equation based on a moment-system approximation in velocity dependence and a discontinuous Galerkin finite-element (DGFE) approximation in position dependence. We derive computable error estimates and bounds for general target functionals of solutions of the steady Boltzmann equation based on the DGFE moment approximation. The a-posteriori error estimates and bounds are used to guide a model adaptive algorithm for optimal approximations of the goal functional in question. We present results for one-dimensional heat transfer and shock structure problems where the moment model order is refined locally in space for optimal approximation of the heat flux.

Original language	English
Pages (from-to)	219-239
Number of pages	21
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	325
DOIs	https://doi.org/10.1016/j.cma.2017.06.024
Publication status	Published - 1 Oct 2017

Keywords

A-posteriori error estimation
Boltzmann equation
Discontinuous Galerkin finite element methods
Goal-oriented model adaptivity
Hyperbolic systems
Moment systems

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10.1016/j.cma.2017.06.024

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title = "Error estimation and adaptive moment hierarchies for goal-oriented approximations of the Boltzmann equation",

abstract = "This paper presents an a-posteriori goal-oriented error analysis for a numerical approximation of the steady Boltzmann equation based on a moment-system approximation in velocity dependence and a discontinuous Galerkin finite-element (DGFE) approximation in position dependence. We derive computable error estimates and bounds for general target functionals of solutions of the steady Boltzmann equation based on the DGFE moment approximation. The a-posteriori error estimates and bounds are used to guide a model adaptive algorithm for optimal approximations of the goal functional in question. We present results for one-dimensional heat transfer and shock structure problems where the moment model order is refined locally in space for optimal approximation of the heat flux.",

keywords = "A-posteriori error estimation, Boltzmann equation, Discontinuous Galerkin finite element methods, Goal-oriented model adaptivity, Hyperbolic systems, Moment systems",

author = "M.R.A. Abdelmalik and {van Brummelen}, E.H.",

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AU - van Brummelen, E.H.

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N2 - This paper presents an a-posteriori goal-oriented error analysis for a numerical approximation of the steady Boltzmann equation based on a moment-system approximation in velocity dependence and a discontinuous Galerkin finite-element (DGFE) approximation in position dependence. We derive computable error estimates and bounds for general target functionals of solutions of the steady Boltzmann equation based on the DGFE moment approximation. The a-posteriori error estimates and bounds are used to guide a model adaptive algorithm for optimal approximations of the goal functional in question. We present results for one-dimensional heat transfer and shock structure problems where the moment model order is refined locally in space for optimal approximation of the heat flux.

AB - This paper presents an a-posteriori goal-oriented error analysis for a numerical approximation of the steady Boltzmann equation based on a moment-system approximation in velocity dependence and a discontinuous Galerkin finite-element (DGFE) approximation in position dependence. We derive computable error estimates and bounds for general target functionals of solutions of the steady Boltzmann equation based on the DGFE moment approximation. The a-posteriori error estimates and bounds are used to guide a model adaptive algorithm for optimal approximations of the goal functional in question. We present results for one-dimensional heat transfer and shock structure problems where the moment model order is refined locally in space for optimal approximation of the heat flux.

KW - A-posteriori error estimation

KW - Boltzmann equation

KW - Discontinuous Galerkin finite element methods

KW - Goal-oriented model adaptivity

KW - Hyperbolic systems

KW - Moment systems

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DO - 10.1016/j.cma.2017.06.024

M3 - Article

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SN - 0045-7825

VL - 325

SP - 219

EP - 239

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

ER -

Error estimation and adaptive moment hierarchies for goal-oriented approximations of the Boltzmann equation

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Keywords

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