Error Estimates for Finite Volume Approximations of Classical Solutions for Nonlinear Systems of Hyperbolic Balance Laws

SIAM Journal on Numerical Analysis ◽

10.1137/s0036142903438136 ◽

2006 ◽

Vol 43 (6) ◽

pp. 2423-2449 ◽

Author(s):

Vladimir Jovanovic ◽

Christian Rohde

Keyword(s):

Nonlinear Systems ◽

Error Estimates ◽

Finite Volume ◽

Classical Solutions ◽

Balance Laws ◽

Hyperbolic Balance Laws

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Finite volume schemes for hyperbolic balance laws with multiplicative noise

Applied Numerical Mathematics ◽

10.1016/j.apnum.2011.01.011 ◽

2012 ◽

Vol 62 (4) ◽

pp. 441-456 ◽

Author(s):

I. Kröker ◽

C. Rohde

Keyword(s):

Finite Volume ◽

Multiplicative Noise ◽

Balance Laws ◽

Finite Volume Schemes ◽

Hyperbolic Balance Laws

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Multi-level Monte Carlo Finite Volume Methods for Uncertainty Quantification in Nonlinear Systems of Balance Laws

Uncertainty Quantification in Computational Fluid Dynamics - Lecture Notes in Computational Science and Engineering ◽

10.1007/978-3-319-00885-1_6 ◽

2013 ◽

pp. 225-294 ◽

Author(s):

Siddhartha Mishra ◽

Christoph Schwab ◽

Jonas Šukys

Keyword(s):

Monte Carlo ◽

Nonlinear Systems ◽

Uncertainty Quantification ◽

Finite Volume ◽

Finite Volume Methods ◽

Balance Laws ◽

Systems Of Balance Laws ◽

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Consistency of finite volume approximations to nonlinear hyperbolic balance laws

Mathematics of Computation ◽

10.1090/mcom/3569 ◽

2020 ◽

Vol 90 (327) ◽

pp. 141-169

Author(s):

Matania Ben-Artzi ◽

Jiequan Li

Keyword(s):

Finite Volume ◽

Balance Laws ◽

Hyperbolic Balance Laws

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High order well-balanced finite volume methods for multi-dimensional systems of hyperbolic balance laws

Computers & Fluids ◽

10.1016/j.compfluid.2021.104858 ◽

2021 ◽

Vol 219 ◽

pp. 104858

Author(s):

Jonas P. Berberich ◽

Praveen Chandrashekar ◽

Christian Klingenberg

Keyword(s):

Finite Volume ◽

Finite Volume Methods ◽

Balance Laws ◽

Hyperbolic Balance Laws

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Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws

Journal of Computational Physics ◽

10.1016/j.jcp.2007.12.005 ◽

2008 ◽

Vol 227 (8) ◽

pp. 3971-4001 ◽

Author(s):

Michael Dumbser ◽

Cedric Enaux ◽

Eleuterio F. Toro

Keyword(s):

Finite Volume ◽

Balance Laws ◽

Finite Volume Schemes ◽

Order Of Accuracy ◽

Hyperbolic Balance Laws ◽

High Order Of Accuracy ◽

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A priori error estimates of a Jacobi spectral method for nonlinear systems of fractional boundary value problems and related Volterra-Fredholm integral equations with smooth solutions

Numerical Algorithms ◽

10.1007/s11075-019-00743-5 ◽

2019 ◽

Vol 84 (1) ◽

pp. 63-89 ◽

Author(s):

Mahmoud A. Zaky ◽

Ibrahem G. Ameen

Keyword(s):

Nonlinear Systems ◽

Boundary Value Problems ◽

Integral Equations ◽

Spectral Method ◽

Error Estimates ◽

A Priori ◽

Fredholm Integral Equations ◽

Smooth Solutions ◽

Priori Error Estimates ◽

Fractional Boundary Value Problems

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Uniqueness of Solutions to Hyperbolic Balance Laws in Several Space Dimensions

Communications in Partial Differential Equations ◽

10.1080/03605308908820638 ◽

1989 ◽

Vol 14 (8-9) ◽

pp. 959-979 ◽

Author(s):

Hermano Frid

Keyword(s):

Balance Laws ◽

Uniqueness Of Solutions ◽

Hyperbolic Balance Laws

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Hyperbolic balance laws: Riemann invariants and the generalized Riemann problem

Numerische Mathematik ◽

10.1007/s00211-007-0069-y ◽

2007 ◽

Vol 106 (3) ◽

pp. 369-425 ◽

Author(s):

Matania Ben-Artzi ◽

Jiequan Li

Keyword(s):

Riemann Problem ◽

Balance Laws ◽

Riemann Invariants ◽

Generalized Riemann Problem ◽

Hyperbolic Balance Laws

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Application: Oscillatory Profiles in Systems of Hyperbolic Balance Laws

Bifurcation without Parameters - Lecture Notes in Mathematics ◽

10.1007/978-3-319-10777-6_7 ◽

2014 ◽

pp. 49-54

Author(s):

Stefan Liebscher

Keyword(s):

Balance Laws ◽

Hyperbolic Balance Laws

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Analysis of the Zero Relaxation Limit of Hyperbolic Balance Laws with Random Initial Data

SIAM/ASA Journal on Uncertainty Quantification ◽

10.1137/18m1226683 ◽

2019 ◽

Vol 7 (3) ◽

pp. 806-837

Author(s):

James M. Scott ◽

M. Paul Laiu ◽

Cory D. Hauck

Keyword(s):

Initial Data ◽

Balance Laws ◽

Random Initial Data ◽

Hyperbolic Balance Laws

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