- E. Tadmor
Skew self-adjoint form for systems of conservation
laws
Journal of Mathematical Analysis and Applications 103(2)
(1984) 428-442.
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 |
- E. Tadmor
Numerical viscosity and the entropy condition for
conservative difference schemes
Mathematics of Computation 43
(1984) 369-381.
|
|
- E. Tadmor
A minimum entropy principle in the gas dynamics
equations
Applied Numerical Mathematics 2 (1986)
211-219.
|
|
- E. Tadmor
Entropy conservative finite element schemes
in
"Numerical Methods for Compressible Flows - Finite Difference Element and Volume
Techniques", Proceedings of the winter annual meeting of the American Society of
Mechanical Engineering, Vol. AMD-Vol. 78 (T. E. Tezduyar and T.J.R. Hughes, eds.)
(1986) 149-158..
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- E. Tadmor
Entropy functions for symmetric systems of conservation
laws
Journal of Mathematical Analysis and Applications 122(2)
(1987) 355-359.
|
|
- E. Tadmor
The entropy dissipation by numerical viscosity in nonlinear
conservative difference schemes
in "Nonlinear Hyperbolic Problems'",
Proceedings of a 1986 Advanced Research Workshop in St. Etienne, Lecture Notes in
Mathematics, Vol. Vol. 1270 (C. Carasso, P.-A. Raviart and D. Serre, eds.),
Springer-Verlag (1987) 52-63..
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|
- E. Tadmor
The numerical viscosity of entropy stable schemes for systems
of conservation laws. I.
Mathematics of Computation 49 (1987)
91-103.
|
|
- M. Merriam
An entropy based approach to nonlinear
stability
NASA Technical Memorandum 101086 (1989).
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|
- F. Dubois
Concavity of thermostatic entropy and convexity of LAX's
mathematical entropy
La Recherche Aerospatiale (English Edition)
(ISSN 0379-380X) 3 (1990) 77-80.
|
|
- Brahim Khobalatte and Benoit Perthame
Maximum principle on the entropy
and second-order kinetic schemes
Mathematics of Computation
62(205) (1994) 118-131.
|
|
- F. Bouchut, Ch. Bourdarias and B. Perthame
A MUSCL method satisfying
all the numerical entropy inequalities
Mathematics of
Computation 65 (1996) 65 (1996), 1439-1461.
|
|
- B. Hayes and P. LeFloch
Nonclassical shocks and kinetic relations:
finite difference schemes
SIAM J. Numerical Analysis 35(6)
(1998) 2169-2194.
|
|
- C. Rhode and P. LeFloch
High-order schemes, entropy inequalities, and
nonclassical shocks
SIAM J. Numerical Analysis 37(6) (2000)
2023-2060.
|
|
- C. Chalons and P. LeFloch
High-order entropy-conservative schemes and
kinetic relations for van der Waals fluids
Journal of
Computational Physics 168(1) (2001) 184-206.
|
|
- C. Chalons and P. LeFloch
A fully discrete scheme for
diffusive-dispersive conservation laws
Numerische Mathematik
89(3) (2001) 493-509.
|
|
- C. Chalons and P. G. LeFloch
High-order entropy-conservative schemes
and kinetic relations for van der Waals fluids
Journal of
Computational Physics 168(1) (2001) 184-2006.
|
|
- P. LeFloch, J.M. Mercier and C. Rohde
Fully discrete, entropy
conservative schemes of arbitrary order
SIAM J. Numerical
Analysis 40(5) (2002) 1968-1992.
|
|
- E. Tadmor
Entropy stability theory for difference approximations of
nonlinear conservation laws and related time dependent
problems
Acta Numerica 12 (2003) 451-512.
|
|
- R. Abramov and J. Majda
Discrete approximations with additional
conserved quantities: deterministic and statistical
behavior
Methods and Applications in Analysis 10(2) (2003)
151-189.
|
|
- G. F. Naterer and J. A. Camberos
Entropy and the second law fluid flow
and heat transfer simulation
AIAA Journal of Thermophysics and
Heat Transfer 17(3) (2003) 360-371.
|
|
- E. Tadmor and W. Zhong
Entropy stable approximations of Navier-Stokes
equations with no artificial numerical viscosity
J. of Hyperbolic
Differential Equations 3(3) (2006) 529-559.
|
|
- E. Tadmor
On the entropy stability of difference schemes: a comparison
principle and a homotopy approach
in "Hyperbolic Problems: Theory,
Numerics, Applications'", Proceedings of the 10th International Conference in 2004,
Vol. vol. I (F. Asukura, H. Aiso, S. Kawashima, A. Matsumura, S. Nishibata & K.
Nishihara, eds.), Yokohama Publishers, Osaka (2006) 195-204..
|
|
- P. Roe
Affordable, entropy-consistent, Euler flux functions (with
applications to the carbuncle phenomenon)
in "11th International
Conference on `Hyperbolic Problems: Theory, Numerics, Applications'", Lyon
(2006).
|
|
- E. Tadmor and W. Zhong
Novel entropy stable schemes for 1D and 2D fluid
equations
in "Hyperbolic Problems: Theory, Numerics, Applications",
Proceedings of the 11th International Conference in Lyon in 2006 (S. Benzoni-Gavage
and D. Serre, eds.), Springer (2007) 1111-1120..
|
|
- J. Haink and C. Rohde
Local discontinuous-Galerkin schemes for model
problems in phase transition theory
Communications in
Computational Physics 4(4) (2008) 860-893.
|
|
- P. LeFloch and M. Mohammadian
Why many theories of shock waves are
necessary: kinetic functions, equivalent equations, and fourth-order
models
J. Computational Physics 227(8) (2008)
4162-4189.
|
|
- D. Kroner, P. LeFloch and M.-D. Thanh
The minimum entropy principle for
compressible fluid flows in a nozzle with discontinuous
cross-section
Mathematical Modeling & Numerical Analysis
42(3) (2008) 425-442.
|
|
- E. Tadmor and W. Zhong
Energy-preserving and stable approximations for
the two-dimensional shallow water equations
in "Mathematics and
Computation - A Contemporary View", Proceedings of the Third Abel Symposium held in
Alesund, Norway in 2006 (H. Munthe-Kaas & B. Owren eds.), Springer (2008)
67-94..
|
|
- Jean-Luc Guermond and Richard Pasquetti
Entropy-based nonlinear
viscosity for Fourier approximations of conservation laws
C. R.
Acad. Sci. Paris, Ser. I 346 (2008) 801-806.
|
|
- J. M. Mercier
Optimally transported schemes: one dimensional
case
(2008).
|
|
- P. LeFloch and S. Mishra
Kinetic functions in magnetohydrodynamics with
resistivity and Hall effect
Acta Mathematica Scientia 29B(6)
(2009) 1684-1702.
|
|
- K. Kitamura, P. Roe and F. Ismail
Evaluation of Euler fluxes for
hypersomic flow computations
AIAA 47(1) (2009) 44-53.
|
|
- M. Lukacova- Medvidova and K. W. Morton
Finite volume evolution
Galerkin methods: A survey
Indian J. Pure & Appl. Math.
(2009).
|
|
- B. Sjogreen and H. Yee
On skew-symmetric splitting and entropy
conservation for the Euler Equations
in "Numerical Mathematics and
Advanced Applications", Proc of ENUMATH2009 8th European Conference held in Uppsala
in 2009 (G. Kreiss, P. Lotstedt, A. Malquist, M. Neytcheva eds.), Springer (2009)
817-827..
|
|
- U. Fjordholm, S. Mishra and E. Tadmor
Energy preserving and energy
stable schemes for the shallow water equations
in "Foundations of
Computational Mathematics", Proc. FoCM in 2008 (F. Cucker, A. Pinkus & M. Todd,
eds), London Math. Soc. Lecture Notes Ser. 363, Hong Kong (2009) 93-139..
|
|
- M. Lukacova- Medvidova and E. Tadmor
On the entropy stability of
Roe-type finite volume methods
in "Hyperbolic Problems: Theory,
Numerics, Applications", Proceedings of the 12th International Conference in 2008,
Vol. 67(2) (E. Tadmor, J.-G. Liu & A. Tzavaras, eds.), AMS Proc. Symp. Applied
Math., University of Maryland (2009) 765-774..
|
|
- Aziz Madrane and Eitan Tadmor
Entropy stability of Roe-type upwind
finite volume methods on unstructured grids
in "Hyperbolic Problems:
Theory, Numerics, Applications", Proceedings of the 12th International Conference in
2008, Vol. 67(2) (E. Tadmor, J.-G. Liu & A. Tzavaras, eds.), AMS Proc. Symp. Applied
Math., University of Maryland (2009) 775-784..
|
|
- Susana Serna
A characteristic-based nonconvex entropy fix upwind scheme
for the ideal magnetohydrodynamic equations
Journal of
Computational Physics 228 (2009) 4232-4247.
|
|
- F. Ismail and P. L. Roe
Affordable, entropy-consistent Euler flux
functions II: Entropy production at shocks
J. Computational
Physics 228 (2009) 5410-5436.
|
|
- Christos Arvanitis, Charalambos Makridakis and Nikolaos
Sfakianakis
Entropy conservative schemes and adapive mesh selection for
hyperbolic conservation laws
Journal of Hyperbolic Differential
Equations 7(3) (2010) 383-404.
|
|
- Jean-Luc Guermond and Richard Pasquetti
Entropy viscosity method for
high-order approximations of conservation laws
in "Spectral and High
Order Methods for Partial Differential Equations (ICOSAHOM)", Lecture Notes in
computational Science and Engineering, Vol. 76 (Jan S. Hesthaven and Einar M.
Ronquist, eds.), Springer, Trondheim, Norway, June 2009 (2011) 411-418..
|
|
- U. Fjordholm, S. Mishra and E. Tadmor
Well-balanced and energy stable
schemes for the shallow water equations with discontinuous
topography
J. Computational Physics 230(14) (2011)
5587-5609.
|
|
- Jean-Luc Guermond, Richard Pasquetti and Bojan Popov
Entropy viscosity
method for nonlinear conservation laws
Journal of Computational
Physics 230(11) (2011) 4248-4267.
|
|
- Ulrik S. Fjordholm
Energy conservative and stable schemes for the
two-layer shallow water equations
in "Hyperbolic problems: Theory,
Numerics and Applications", Vol. 2 (Tatsien Li and Song Jiang, eds.), Higher
Education Press, Beijing, June 2010 (2011) 414-421..
|
|
- Gabriella Puppo and Matteo Semplice
Numerical entropy and adaptivity
for finite volume schemes
Communications in Computational
Physics 10(5) (2011) 1132-1160.
|
|
- U. Fjordholm and S. Mishra
Accurate numerical discretizations of
non-conservative hyperbolic systems
Mathematical Modelling and
Numerical Analysis 46(1) (2011) 187-206.
|
|
- Gabriella Puppo and Matteo Semplice
Entropy and the numerical
integration of conservation laws
Physics Procedia (2011)
1-28.
|
|
- H. Kumar and S. Mishra
Enropy stable numerical schemes for two-fluid
plasma equations
Journal of Scientific Computing 52 (2011)
401-425.
|
|
- Xiangxiong Zhang and Chi-Wang Shu
A minimum entropy principle of high
order schemes for gas dynamics equations
Numerische
Mathematik 121 (2011) 545-563.
|
|
- U. Fjordholm, S. Mishra and E. Tadmor
Arbitrarily high order accurate
entropy stable essentially non-oscillatory schemes for systems of conservation
laws
SIAM Journal on Numerical Analysis 50(2) (2012)
544-573.
|
|
- M. Svärd and S. Mishra
Entropy stable schemes for
initial-boundary-value conservation laws
Zeitschrift für
angewandte Mathematik und Physik (ZAMP) (2012).
|
|
- A. Mardane, U. Fjordholm, S. Mishra and E. Tadmor
Entropy conservative
and entropy stable finite volume schemes for multi-dimensional conservation laws
on unstructured meshes,
in "European Congress Computational Methods
Applied Sciences and Engineering", Prceedings of ECCOMAS 2012 (J. Eberhardsteiner
et. al. eds.), held in Vienna (2012).
|
|
- A. N. Mohammed and F. Ismail
Study of an entropy-consistent
Navier-Stokes flux
International Journal of Computational Fluid
Dynamics 27(1) (2012) 1-14.
|
|
- Manuel J. Castro, Ulrik S. Fjordholm, Siddhartha Mishra and Carlos
Parés
Entropy conservative and entropy stable schemes for
nonconservative hyperbolic systems
SIAM J. Numerical Analysis
51(3) (2012) 1371-1391.
|
|
- A. Hiltebrand and S. Mishra
Entropy stable shock capturing space-time
discontinuous Galerkin schemes for systems of conservation
laws
Numerische Mathematik 126(1) (2013) 103-151.
|
|
- Mark H. Carpenter and Travis C. Fisher
High-order entropy stable
formulations for computational fluid dynamics
in "21st AIAA
Computational Fluid Dynamics Conference", San-Diego, CA (2013) AIAA
2013-2868..
|
|
- Praveen Chandrashekar
Kinetic energy preserving and entropy stable
finite volume schemes for compressible Euler and Navier-Stokes
equations
Communications in Computational Physics 14(5)
(2013) 1252-1286.
|
|
- Magnus Svard and Hatice Ozcan
Entropy-stable schemes for the Euler
equations with far-field and wall boundary conditions
Journal of
Scientific Computing 58(1) (2014) 61-89.
|
|
- Jean-Luc Guermond and Bojan Popov
Viscous regularization of the Euler
equations and entropy principles
SIAM J. Applied Math 74(2)
(2014) 284-305.
|
|
- M. Lukacova-Medvidova and N. Sfakianakis
Entropy dissipation of moving
mesh adaptation
J. Hyperbolic Differential Equations
(2014).
|
|
- Jean-Luc Guermond and Bojan Popov
Entropy viscosity for the Euler
equations and questions regarding parabolic regularization .
in
"Hyperbolic Problems: Hyperbolic Problems: Theory, Numerics, Applications", held in
Padova in 2012 (Fabio Ancona, Alberto Bressan, Pierangelo Marcati, Andrea Marson
eds.), AIMS on Applied Mathematics Vol. 8(1) (2014) 119-124..
|
|
- Philippe LeFloch and Sid Mishra
Numerical methods with controlled
dissipation for small-scale dependent shocks
Acta Numerica 23
(2014) 743-816.
|
|
- A. N. Gorban and D. J. Packwood
Enhancement of the stability of lattice
Boltzmann methods by dissipation control
Physica A 414 (2014)
285-299.
|
|
- A. N. Mohammed and F. Ismail
Entropy consistent methods for the
Navier-Stokes equations. A first-order systems approach
J.
Scientific Computation 63 (2014) 612-631.
|
 |
- Laslo T. Diosadyand and Scott M. Murman and Scott M.
Murman
Higher-order methods for compressible turbulent flows using
entropy variables
in "53rd AIAA Aerospace Sciences Meeting" in 2015,
Vol. 2015-0294, Kissimmee, FL (2015).
|
|
- Yu Lv and Matthias Ihme
Entropy-bounded discontinuous Galerkin scheme
for Euler equations
Journal of Computational Physics 295
(2015) 715739.
|
|
- Siddhartha Mishra and Laura V. Spinolo
Accurate numerical schemes for
approximating initial-boundary value problems for systems of conservation
laws
Journal of Hyperbolic Differential Equations 12 (2015)
61-86.
|
|
- U. Fjordholm, R. Kappeli, S. Mishra and E. Tadmor
Construction of
approximate entropy measure valued solutions for systems of conservation
laws
Foundations of Computational Mathematics 17 (2015)
763-827.
|
|
- S. Lanthaler and S. Mishra
Computation of measure valued solutions for
the incompressible Euler equations
Mathematical Models and Methods
in Applied Sciences (2015).
|
|
- M. Parsani, M. H. Carpenter and E. J. Nielsen
Entropy stable wall
boundary conditions for the three-dimensional compressible Navier-Stokes
equations
Journal of Computational Physics 292 (2015)
88-113.
|
|
- A. R. Winters and G. J. Gassner
Affordable, entropy conserving and
entropy stable flux functions for the ideal MHD equations
Journal
of Computational Physics 304 (2015) 72-108.
|
|
- E. Tadmor
Perfect derivatives, conservative differences and entropy
stable computation of hyperbolic conservation laws
Discrete and
Continuous Dynamical Systems-A 36(8) (2016) 4579-4598.
|
|
- M. Zakerzadeh and G. May
On the convergence of a shock capturing
discontinuous Galerkin method for nonlinear hyperbolic systems of conservation
laws
SIAM J. Numerical Analysis 54(2) (2016) 874-898.
|
|
- D. Ray, P. Chandrashekar, U. S. Fjordholm and S. Mishra
Entropy stable
scheme on two-dimensional unstructured grids for Euler
equations
Communications in Computational Physics 19(5)
(2016) 1111-1140.
|
|
- U. S. Fjordholm, S. Mishra and E. Tadmor
On the computation of
measure-valued solutions
Acta Numerica 25 (2016)
567-679.
|
|
- Dominik Derigs, Andrew R. Winters, Gregor J. Gassner and Stefanie
Walch
A novel high-order, entropy stable, 3D AMR MHD solver with
guaranteed positive pressure
Journal of Computational Physics
317 (2016) 223-256.
|
|
- Sudi Mungkasi
Adaptive Finite Volume Method for the Shallow Water
Equations on Triangular Grids
Advances in Mathematical
Physics 2016 (2016).
|
|
- E. Tadmor
Entropy stable schemes
Handbook of Numerical
Methods for Hyperbolic problems XVII (R. Abgrall and C.-W. Shu, eds.),
Elsevier (2016) 467-493.
|
|
- Dominik Derigs, Andrew R. Winters, Gregor J.Gassner and Stefanie
Walch
A novel averaging technique for discrete entropy-stable dissipation
operators for ideal MHD
Journal of Computational Physics 330
(2017) 624-632.
|
|
- Birte Schmidtmann and Andrew R. Winters
Hybrid entropy stable HLL-Type
Riemann solvers for hyperbolic conservation laws
Journal of
Computational Physics 330 (2017) 566-570.
|
|
- Deep Ray
Entropy-stable finite difference and finite volume schemes for
compressible flows
Ph.D. Thesis, TIFR, Bangalore (2017)
1-233.
|
|
- Tianheng Chen and Chi-Wang Shu
Entropy stable high order discontinuous
Galerkin methods with suitable quadrature rules for hyperbolic conservation
laws
Journal of Computational Physics 345 (2017)
427-461.
|
|
- Yong Liu,, Chi-Wang Shu and Mengping Zhang
Entropy stable high order
discontinuous Galerkin methods for ideal compressible MHD on structured
meshes
Journal of Computational Physics 354 (2017)
163-178.
|
|
- J. Crean, J. E.Hicken, D. C.Del Rey Fernández, D.. W. Zingg and M.
Carpenter
Entropy-stable summation-by-parts discretization of the Euler
equations on general curved elements
Journal of Computational
Physics 356(1) (2018) 410-438.
|
|
- Hendrik Ranocha
Comparison of some entropy conservative numerical
fluxes for the Euler equations
Journal of Scientific
Computing 76/1 (2018) 216-242.
|
|
- Ayoub Gouasmi, Scott Murman and Karthik Duraisamy
Entropy conservative
schemes and the receding flow problem
Journal of Scientific
Computing 78(2) (2018) 971-994.
|
|
- Ayoub Gouasmi, Karthik Duraisamy and Scott Murman
On entropy stable
temporal fluxes
ArXiv:1807.03483 (2018).
|
|
- David Williams
An analysis of discontinuous Galerkin methods for the
compressible Euler equations: entropy and L2 stability
Numerische
Mathematik 141(4) (2019) 1079-1120.
|
|
- Jan Hesthaven and Fabian Monkeberg
Entropy stable essentially
non-oscillatory methods based on RBF reconstructions
Mathematical
Modelling and Numerical Analysis 53 (2019) 925-958.
|
|
- T. Chen and C.-W. Shu
Review of entropy stable discontinuous Galerkin
methods for systems of conservation laws on unstructured simplex
meshes
CSIAM Transactions on Applied Mathematics (CSAM).
(2019).
|
|
- K. Wu and C.-W. Shu
Entropy symmetrization and high-order accurate
entropy stable numerical schemes for relativistic MHD
equations
SIAM Journal on Scientific Computing
(2019).
|
|
- Deepak Bhoriya and Harish Kumar
Entropy-stable schemes for relativistic
hydrodynamics equations
Z. Angew. Math. Phys. 71 (2020)
1-29.
|
|
- Ayoub Gouasmi, Karthik Duraisamy and Scott M. Murman
Formulation of
entropy-stable schemes for the multicomponent compressible Euler
equations
Computer Methods in Applied Mechanics and
Engineering 363(1) (2020).
|
|
- Neelabja Chatterjee and Ulrik Skre Fjordholm
Convergence of
second-order, entropy stable methods for multi-dimensional conservation
laws
Mathematical Modelling and Numerical Analysis 54(4)
(2020) 1415 - 1428.
|
|
- Gregor J. Gassner, Magnus Svard and Florian J. Hindenlang
Stability issues of entropy-stable and/or split-form high-order schemes
ArXiv:2007.09026v1 (2020).
|
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