A Note on Adjoint Error Estimation for One-Dimensional Stationary Balance Laws with Shocks

AbstractWe first derive the general error estimate for one – dimensional balance laws and afterwards we apply it to the elastodynamics system with source and to the isentropic Euler system with damping.

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One-Dimensional Systems of Balance Laws (Weakly Coupled)

Understanding Complex Systems - Macroscopic Models for Vehicular Flows and Crowd Dynamics: Theory and Applications ◽

10.1007/978-3-319-00155-5_8 ◽

2013 ◽

pp. 111-120

Author(s):

Massimiliano Daniele Rosini

Keyword(s):

Balance Laws ◽

One Dimensional ◽

Weakly Coupled ◽

Systems Of Balance Laws

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Boundary stabilization in finite time of one-dimensional linear hyperbolic balance laws with coefficients depending on time and space

Journal of Differential Equations ◽

10.1016/j.jde.2020.09.037 ◽

2021 ◽

Vol 271 ◽

pp. 1109-1170

Author(s):

Jean-Michel Coron ◽

Long Hu ◽

Guillaume Olive ◽

Peipei Shang

Keyword(s):

Finite Time ◽

Balance Laws ◽

Boundary Stabilization ◽

Time And Space ◽

One Dimensional ◽

Hyperbolic Balance Laws

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A Moving Finite Element Method with Error Estimation and Refinement for One-Dimensional Time Dependent Partial Differential Equations

SIAM Journal on Numerical Analysis ◽

10.1137/0723050 ◽

1986 ◽

Vol 23 (4) ◽

pp. 778-796 ◽

Cited By ~ 82

Author(s):

Slimane Adjerid ◽

Joseph E. Flaherty

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Partial Differential Equations ◽

Differential Equations ◽

Error Estimation ◽

Time Dependent ◽

Partial Differential ◽

One Dimensional ◽

Element Method ◽

Moving Finite Element

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Asymptotic-numerical solution of nonlinear systems of one-dimensional balance laws

Journal of Computational Physics ◽

10.1016/j.jcp.2013.02.030 ◽

2013 ◽

Vol 245 ◽

pp. 347-363 ◽

Cited By ~ 2

Author(s):

Danilo Costarelli ◽

Matteo Laurenzi ◽

Renato Spigler

Keyword(s):

Nonlinear Systems ◽

Numerical Solution ◽

Balance Laws ◽

One Dimensional

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A posteriori error estimation with finite element methods of lines for one-dimensional parabolic systems

Numerische Mathematik ◽

10.1007/bf01385737 ◽

1993 ◽

Vol 65 (1) ◽

pp. 1-21 ◽

Cited By ~ 31

Author(s):

Slimane Adjerid ◽

Joseph E. Flaherty ◽

Yun J. Wang

Keyword(s):

Finite Element ◽

Error Estimation ◽

Finite Element Methods ◽

Parabolic Systems ◽

Posteriori Error ◽

A Posteriori Error Estimation ◽

A Posteriori ◽

Posteriori Error Estimation ◽

A Posteriori Error ◽

One Dimensional

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Error Estimation of Numerical Solutions of One-dimensional Burgers Equation by Adjoint Sensitivity Analysis Method

TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series B ◽

10.1299/kikaib.71.2256 ◽

2005 ◽

Vol 71 (709) ◽

pp. 2256-2263

Author(s):

Nobuatsu TANAKA ◽

Yasunori MOTOYAMA

Keyword(s):

Sensitivity Analysis ◽

Error Estimation ◽

Numerical Solutions ◽

Burgers Equation ◽

Adjoint Sensitivity Analysis ◽

Analysis Method ◽

Adjoint Sensitivity ◽

One Dimensional ◽

Sensitivity Analysis Method

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The complex-power error-estimation criteria for one-dimensional wave propagation problems

IRE Transactions on Antennas and Propagation ◽

10.1109/tap.1981.1142608 ◽

1981 ◽

Vol 29 (3) ◽

pp. 544-547 ◽

Cited By ~ 1

Author(s):

Chun Chen ◽

Yean-Woei Kiang ◽

Chuen-Der Lien

Keyword(s):

Wave Propagation ◽

Error Estimation ◽

One Dimensional ◽

Complex Power ◽

Dimensional Wave

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