An Integrated Quadratic Reconstruction for Finite Volume Schemes to Scalar Conservation Laws in Multiple Dimensions

Li Chen

doi:10.4208/csiam-am.2020-0017

An Integrated Quadratic Reconstruction for Finite Volume Schemes to Scalar Conservation Laws in Multiple Dimensions

CSIAM Transactions on Applied Mathematics ◽

10.4208/csiam-am.2020-0017 ◽

2020 ◽

Vol 1 (3) ◽

pp. 437-463

Author(s):

Li Chen

Keyword(s):

Conservation Laws ◽

Finite Volume ◽

Scalar Conservation Laws ◽

Finite Volume Schemes ◽

Multiple Dimensions ◽

Scalar Conservation

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Convergence of Upwind Finite Volume Schemes for Scalar Conservation Laws in Two Dimensions

SIAM Journal on Numerical Analysis ◽

10.1137/0731017 ◽

1994 ◽

Vol 31 (2) ◽

pp. 324-343 ◽

Cited By ~ 40

Author(s):

Dietmar Kröner ◽

Mirko Rokyta

Keyword(s):

Conservation Laws ◽

Finite Volume ◽

Two Dimensions ◽

Scalar Conservation Laws ◽

Finite Volume Schemes ◽

Scalar Conservation

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Convergence and error estimates in finite volume schemes for general multidimensional scalar conservation laws. I. Explicite monotone schemes

ESAIM Mathematical Modelling and Numerical Analysis ◽

10.1051/m2an/1994280302671 ◽

1994 ◽

Vol 28 (3) ◽

pp. 267-295 ◽

Cited By ~ 43

Author(s):

J.-P. Vila

Keyword(s):

Conservation Laws ◽

Error Estimates ◽

Finite Volume ◽

Scalar Conservation Laws ◽

Finite Volume Schemes ◽

Monotone Schemes ◽

Scalar Conservation

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Finite volume schemes with equilibrium type discretization of source terms for scalar conservation laws

Journal of Computational Physics ◽

10.1016/s0021-9991(03)00086-x ◽

2003 ◽

Vol 187 (2) ◽

pp. 391-427 ◽

Cited By ~ 21

Author(s):

Ramaz Botchorishvili ◽

Olivier Pironneau

Keyword(s):

Conservation Laws ◽

Finite Volume ◽

Source Terms ◽

Scalar Conservation Laws ◽

Finite Volume Schemes ◽

Scalar Conservation

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Convergence of monotone finite volume schemes for hyperbolic scalar conservation laws with multiplicative noise

Stochastic Partial Differential Equations Analysis and Computations ◽

10.1007/s40072-015-0052-z ◽

2015 ◽

Vol 4 (1) ◽

pp. 150-223 ◽

Cited By ~ 1

Author(s):

C. Bauzet ◽

J. Charrier ◽

T. Gallouët

Keyword(s):

Conservation Laws ◽

Finite Volume ◽

Multiplicative Noise ◽

Scalar Conservation Laws ◽

Finite Volume Schemes ◽

Scalar Conservation

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Convergence of higher order upwind finite volume schemes on unstructured grids for scalar conservation laws in several space dimensions

Numerische Mathematik ◽

10.1007/s002110050156 ◽

1995 ◽

Vol 71 (4) ◽

pp. 527-560 ◽

Cited By ~ 33

Author(s):

Dietmar Kröner ◽

Sebastian Noelle ◽

Mirko Rokyta

Keyword(s):

Conservation Laws ◽

Finite Volume ◽

Unstructured Grids ◽

Higher Order ◽

Scalar Conservation Laws ◽

Finite Volume Schemes ◽

Scalar Conservation

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Finite volume schemes for nonhomogeneous scalar conservation laws: error estimate

Numerische Mathematik ◽

10.1007/pl00005452 ◽

2001 ◽

Vol 88 (4) ◽

pp. 607-639 ◽

Cited By ~ 8

Author(s):

Claire Chainais-Hillairet ◽

Sylvie Champier

Keyword(s):

Error Estimate ◽

Conservation Laws ◽

Finite Volume ◽

Scalar Conservation Laws ◽

Finite Volume Schemes ◽

Scalar Conservation

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Convergence of flux-splitting finite volume schemes for hyperbolic scalar conservation laws with a multiplicative stochastic perturbation

Mathematics of Computation ◽

10.1090/mcom/3084 ◽

2016 ◽

Vol 85 (302) ◽

pp. 2777-2813 ◽

Cited By ~ 11

Author(s):

C. Bauzet ◽

J. Charrier ◽

T. Gallouët

Keyword(s):

Conservation Laws ◽

Finite Volume ◽

Stochastic Perturbation ◽

Scalar Conservation Laws ◽

Finite Volume Schemes ◽

Flux Splitting ◽

Scalar Conservation

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Convergence of the Finite Volume method for scalar conservation laws with multiplicative noise: an approach by kinetic formulation

Stochastic Partial Differential Equations Analysis and Computations ◽

10.1007/s40072-019-00146-6 ◽

2019 ◽

Vol 8 (2) ◽

pp. 265-310 ◽

Cited By ~ 1

Author(s):

Sylvain Dotti ◽

Julien Vovelle

Keyword(s):

Conservation Laws ◽

Finite Volume Method ◽

Finite Volume ◽

Multiplicative Noise ◽

Scalar Conservation Laws ◽

Kinetic Formulation ◽

Scalar Conservation ◽

Volume Method

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Convergence of finite volume monotone schemes for scalar conservation laws on bounded domains

Numerische Mathematik ◽

10.1007/s002110100307 ◽

2002 ◽

Vol 90 (3) ◽

pp. 563-596 ◽

Cited By ~ 39

Author(s):

Julien Vovelle

Keyword(s):

Conservation Laws ◽

Finite Volume ◽

Bounded Domains ◽

Scalar Conservation Laws ◽

Monotone Schemes ◽

Scalar Conservation

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A finite volume method for scalar conservation laws with stochastic time–space dependent flux functions

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2012.07.014 ◽

2013 ◽

Vol 237 (1) ◽

pp. 614-632 ◽

Cited By ~ 10

Author(s):

Kamel Mohamed ◽

Mohammed Seaid ◽

Mostafa Zahri

Keyword(s):

Conservation Laws ◽

Finite Volume Method ◽

Finite Volume ◽

Scalar Conservation Laws ◽

Time Space ◽

Scalar Conservation ◽

Volume Method ◽

Stochastic Time

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