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Volumn 68, Issue 227, 1999, Pages 955-970

Convergence of relaxation schemes for hyperbolic conservation laws with stiff source terms

Author keywords

Conservation laws; Entropy solution; Fully implicit scheme; MUSCL method; Relaxation scheme; Semi implicit scheme; Stiff source term; TVD scheme

Indexed keywords


EID: 0006388461     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0025-5718-99-01089-3     Document Type: Article
Times cited : (30)

References (60)
  • 1
    • 85065353078 scopus 로고    scopus 로고
    • Convergence of relaxation schemes for conservation laws
    • D. Aregba-Driollet and R. Natalini, Convergence of relaxation schemes for conservation laws, Appl. Anal. 61 (1996), 163-193. CMP 98:13
    • (1996) Appl. Anal. , vol.61 , pp. 163-193
    • Aregba-Driollet, D.1    Natalini, R.2
  • 2
    • 85065353078 scopus 로고    scopus 로고
    • D. Aregba-Driollet and R. Natalini, Convergence of relaxation schemes for conservation laws, Appl. Anal. 61 (1996), 163-193. CMP 98:13
    • CMP , vol.98 , pp. 13
  • 4
    • 0028534347 scopus 로고    scopus 로고
    • Upwind methods for hyperbolic conservation laws with source terms
    • A. Bermudez and M. E. Vazquez, Upwind methods for hyperbolic conservation laws with source terms, Comput. & Fluids, 23 (1994), pp. 1049-1071. MR 95i:76065
    • (1994) Comput. & Fluids , vol.23 , pp. 1049-1071
    • Bermudez, A.1    Vazquez, M.E.2
  • 5
    • 0028534347 scopus 로고    scopus 로고
    • A. Bermudez and M. E. Vazquez, Upwind methods for hyperbolic conservation laws with source terms, Comput. & Fluids, 23 (1994), pp. 1049-1071. MR 95i:76065
    • MR , vol.95 I , pp. 76065
  • 6
    • 0000757997 scopus 로고    scopus 로고
    • Stable upwind schemes for hyperbolic conservation laws with source terms
    • A. Chalabi, Stable upwind schemes for hyperbolic conservation laws with source terms, IMA J. Numer. Anal., 12 (1992), pp. 217-242. MR 93c:65108
    • (1992) IMA J. Numer. Anal. , vol.12 , pp. 217-242
    • Chalabi, A.1
  • 7
    • 0000757997 scopus 로고    scopus 로고
    • A. Chalabi, Stable upwind schemes for hyperbolic conservation laws with source terms, IMA J. Numer. Anal., 12 (1992), pp. 217-242. MR 93c:65108
    • MR , vol.93 C , pp. 65108
  • 8
    • 0030258570 scopus 로고    scopus 로고
    • An error bound for the polygonal approximation of conservation laws with source terms
    • A. Chalabi, An error bound for the polygonal approximation of conservation laws with source terms, Comput. & Math. Appl., 32 (1996), pp. 59-63. MR 97i:65143
    • (1996) Comput. & Math. Appl. , vol.32 , pp. 59-63
    • Chalabi, A.1
  • 9
    • 0030258570 scopus 로고    scopus 로고
    • A. Chalabi, An error bound for the polygonal approximation of conservation laws with source terms, Comput. & Math. Appl., 32 (1996), pp. 59-63. MR 97i:65143
    • MR , vol.97 I , pp. 65143
  • 10
    • 0031511378 scopus 로고    scopus 로고
    • On convergence of numerical schemes for hyperbolic conservation laws with stiff source terms
    • A. Chalabi, On convergence of numerical schemes for hyperbolic conservation laws with stiff source terms, Math. Comp., 66 (1997), pp. 527-545. MR 97g:65178
    • (1997) Math. Comp. , vol.66 , pp. 527-545
    • Chalabi, A.1
  • 11
    • 0031511378 scopus 로고    scopus 로고
    • A. Chalabi, On convergence of numerical schemes for hyperbolic conservation laws with stiff source terms, Math. Comp., 66 (1997), pp. 527-545. MR 97g:65178
    • MR , vol.97 G , pp. 65178
  • 12
    • 84990689276 scopus 로고    scopus 로고
    • Hyperbolic conservation laws with stiff relaxation terms and entropy
    • G. Q. Chen, C. D. Levermore and T. P. Liu, Hyperbolic conservation laws with stiff relaxation terms and entropy, Comm. Pure Appl. Math., 47 (1994), pp. 787-830. MR 95h:35133
    • (1994) Comm. Pure Appl. Math. , vol.47 , pp. 787-830
    • Chen, G.Q.1    Levermore, C.D.2    Liu, T.P.3
  • 13
    • 84990689276 scopus 로고    scopus 로고
    • G. Q. Chen, C. D. Levermore and T. P. Liu, Hyperbolic conservation laws with stiff relaxation terms and entropy, Comm. Pure Appl. Math., 47 (1994), pp. 787-830. MR 95h:35133
    • MR , vol.95 H , pp. 35133
  • 14
    • 0001241911 scopus 로고
    • Theoretical and numerical structure for reacting shock waves
    • P. Colella, A. Majda and V. Roytburd, Theoretical and numerical structure for reacting shock waves, SIAM J. Sci. Stat. Comput., 7 (1986), pp. 1059-1080. MR 871:76037
    • (1986) SIAM J. Sci. Stat. Comput. , vol.7 , pp. 1059-1080
    • Colella, P.1    Majda, A.2    Roytburd, V.3
  • 15
    • 0039878542 scopus 로고    scopus 로고
    • P. Colella, A. Majda and V. Roytburd, Theoretical and numerical structure for reacting shock waves, SIAM J. Sci. Stat. Comput., 7 (1986), pp. 1059-1080. MR 871:76037
    • MR , vol.871 , pp. 76037
  • 16
    • 0030532712 scopus 로고    scopus 로고
    • Convergence of the relaxation approximation to a scalar nonlinear hyperbolic equation arising in chromatography
    • J. F. Collet and M. Rascle, Convergence of the relaxation approximation to a scalar nonlinear hyperbolic equation arising in chromatography, Z. Angew. Math. Phys. 47 (1996), 400-409. MR 97d:35132
    • (1996) Z. Angew. Math. Phys. , vol.47 , pp. 400-409
    • Collet, J.F.1    Rascle, M.2
  • 17
    • 0030532712 scopus 로고    scopus 로고
    • J. F. Collet and M. Rascle, Convergence of the relaxation approximation to a scalar nonlinear hyperbolic equation arising in chromatography, Z. Angew. Math. Phys. 47 (1996), 400-409. MR 97d:35132
    • MR , vol.97 D , pp. 35132
  • 18
    • 84966217981 scopus 로고    scopus 로고
    • Monotone difference approximations for scalar conservation conservation laws
    • M. G. Crandall and A. Majda, Monotone difference approximations for scalar conservation conservation laws, Math. Comp., 34 (1980), pp. 1-21. MR 81b:65079
    • (1980) Math. Comp. , vol.34 , pp. 1-21
    • Crandall, M.G.1    Majda, A.2
  • 19
    • 84966217981 scopus 로고    scopus 로고
    • M. G. Crandall and A. Majda, Monotone difference approximations for scalar conservation conservation laws, Math. Comp., 34 (1980), pp. 1-21. MR 81b:65079
    • MR , vol.81 B , pp. 65079
  • 20
    • 0004130037 scopus 로고
    • Robust difference approximations of stiff inviscid detonation waves
    • UCLA, Los Angeles, CA
    • B. Engquist and B. Sjogreen, Robust difference approximations of stiff inviscid detonation waves, CAM report 91-03, UCLA, Los Angeles, CA, 1991.
    • (1991) CAM Report , pp. 91-103
    • Engquist, B.1    Sjogreen, B.2
  • 21
    • 84966209569 scopus 로고    scopus 로고
    • On the accuracy of stable schemes for 2D scalar conservation laws
    • J. B. Goodman and R. Leveque, On the accuracy of stable schemes for 2D scalar conservation laws, Math. Comp., 45 (1985), pp. 15-21. MR 86f:65149
    • (1985) Math. Comp. , vol.45 , pp. 15-21
    • Goodman, J.B.1    Leveque, R.2
  • 22
    • 84966209569 scopus 로고    scopus 로고
    • J. B. Goodman and R. Leveque, On the accuracy of stable schemes for 2D scalar conservation laws, Math. Comp., 45 (1985), pp. 15-21. MR 86f:65149
    • MR , vol.86 F , pp. 65149
  • 23
    • 0001862602 scopus 로고    scopus 로고
    • Runge-Kutta methods for hyperbolic conservation laws with stiff relaxation terms
    • S. Jin, Runge-Kutta methods for hyperbolic conservation laws with stiff relaxation terms, J. Comput. Phys., 122 (1995), pp. 51-67. MR 96g:65084
    • (1995) J. Comput. Phys. , vol.122 , pp. 51-67
    • Jin, S.1
  • 24
    • 0001862602 scopus 로고    scopus 로고
    • S. Jin, Runge-Kutta methods for hyperbolic conservation laws with stiff relaxation terms, J. Comput. Phys., 122 (1995), pp. 51-67. MR 96g:65084
    • MR , vol.96 G , pp. 65084
  • 25
    • 0030147101 scopus 로고    scopus 로고
    • A convex entropy for a hyperbolic system with relaxation
    • S. Jin, A convex entropy for a hyperbolic system with relaxation, J. Diff. Equations, 127 (1996), pp. 97-109. MR 97c:35130
    • (1996) J. Diff. Equations , vol.127 , pp. 97-109
    • Jin, S.1
  • 26
    • 0030147101 scopus 로고    scopus 로고
    • S. Jin, A convex entropy for a hyperbolic system with relaxation, J. Diff. Equations, 127 (1996), pp. 97-109. MR 97c:35130
    • MR , vol.97 C , pp. 35130
  • 27
    • 0030194392 scopus 로고    scopus 로고
    • Numerical schemes for hyperbolic conservation laws with stiff relaxation terms
    • S. Jin and C. D. Levermore, Numerical schemes for hyperbolic conservation laws with stiff relaxation terms, J. Comput. Phys., 126 (1996), pp. 449-467. MR 97g:65173
    • (1996) J. Comput. Phys. , vol.126 , pp. 449-467
    • Jin, S.1    Levermore, C.D.2
  • 28
    • 85190398120 scopus 로고    scopus 로고
    • S. Jin and C. D. Levermore, Numerical schemes for hyperbolic conservation laws with stiff relaxation terms, J. Comput. Phys., 126 (1996), pp. 449-467. MR 97g:65173
    • MR , vol.97 G , pp. 65173
  • 29
    • 84990701264 scopus 로고    scopus 로고
    • The relaxation schemes for systems of conservation laws in arbitrary space dimensions
    • S. Jin and Z. Xin, The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Comm. Pure Appl. Math., 48 (1995), pp. 235-276. MR 96c:65134
    • (1995) Comm. Pure Appl. Math. , vol.48 , pp. 235-276
    • Jin, S.1    Xin, Z.2
  • 30
    • 84990701264 scopus 로고    scopus 로고
    • S. Jin and Z. Xin, The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Comm. Pure Appl. Math., 48 (1995), pp. 235-276. MR 96c:65134
    • MR , vol.96 C , pp. 65134
  • 32
    • 0000220623 scopus 로고
    • First order quasi-linear equations in several independent variables
    • S. N. Kruzkov, First order quasi-linear equations in several independent variables, Math. USSR-Sb., 81 (1970), pp. 228-255. MR 42:2159
    • (1970) Math. USSR-Sb. , vol.81 , pp. 228-255
    • Kruzkov, S.N.1
  • 33
    • 0040380188 scopus 로고    scopus 로고
    • S. N. Kruzkov, First order quasi-linear equations in several independent variables, Math. USSR-Sb., 81 (1970), pp. 228-255. MR 42:2159
    • MR , vol.42 , pp. 2159
  • 34
    • 0000542076 scopus 로고    scopus 로고
    • A study of numerical methods for hyperbolic conservation laws with stiff source terms
    • J. LeVeque and H. C. Yee, A study of numerical methods for hyperbolic conservation laws with stiff source terms, J. Comput. Phys., 86 (1990), pp. 187-210. MR 90k:76009
    • (1990) J. Comput. Phys. , vol.86 , pp. 187-210
    • LeVeque, J.1    Yee, H.C.2
  • 35
    • 0000542076 scopus 로고    scopus 로고
    • J. LeVeque and H. C. Yee, A study of numerical methods for hyperbolic conservation laws with stiff source terms, J. Comput. Phys., 86 (1990), pp. 187-210. MR 90k:76009
    • MR , vol.90 K , pp. 76009
  • 36
    • 21544449601 scopus 로고    scopus 로고
    • Hyperbolic conservation laws with relaxation
    • T. P. Liu, Hyperbolic conservation laws with relaxation, Comm. Math. Phys., 108 (1987), pp. 153-175. MR 88f:35092
    • (1987) Comm. Math. Phys. , vol.108 , pp. 153-175
    • Liu, T.P.1
  • 37
    • 21544449601 scopus 로고    scopus 로고
    • T. P. Liu, Hyperbolic conservation laws with relaxation, Comm. Math. Phys., 108 (1987), pp. 153-175. MR 88f:35092
    • MR , vol.88 F , pp. 35092
  • 38
    • 0019599446 scopus 로고    scopus 로고
    • A qualitative model for dynamic combustion
    • A. Majda, A qualitative model for dynamic combustion, SIAM J. Appl. Math., 40 (1981), pp. 70-93. MR 82j:35096
    • (1981) SIAM J. Appl. Math. , vol.40 , pp. 70-93
    • Majda, A.1
  • 39
    • 0019599446 scopus 로고    scopus 로고
    • A. Majda, A qualitative model for dynamic combustion, SIAM J. Appl. Math., 40 (1981), pp. 70-93. MR 82j:35096
    • MR , vol.82 J , pp. 35096
  • 40
    • 0030490070 scopus 로고    scopus 로고
    • Convergence to equilibrium for the relaxation approximations of conservation laws
    • R. Natalini, Convergence to equilibrium for the relaxation approximations of conservation laws, Comm. Pure Appl. Math. 49 (1996), pp. 795-823. MR 97c:35131
    • (1996) Comm. Pure Appl. Math. , vol.49 , pp. 795-823
    • Natalini, R.1
  • 41
    • 0030490070 scopus 로고    scopus 로고
    • R. Natalini, Convergence to equilibrium for the relaxation approximations of conservation laws, Comm. Pure Appl. Math. 49 (1996), pp. 795-823. MR 97c:35131
    • MR , vol.97 C , pp. 35131
  • 42
    • 0021413939 scopus 로고    scopus 로고
    • Riemann solvers, the entropy condition, and difference approximations
    • S. Osher, Riemann solvers, the entropy condition, and difference approximations, SIAM J. Numer. Anal., 21 (1984), pp. 217-235. MR 86d:65119
    • (1984) SIAM J. Numer. Anal. , vol.21 , pp. 217-235
    • Osher, S.1
  • 43
    • 0021413939 scopus 로고    scopus 로고
    • S. Osher, Riemann solvers, the entropy condition, and difference approximations, SIAM J. Numer. Anal., 21 (1984), pp. 217-235. MR 86d:65119
    • MR , vol.86 D , pp. 65119
  • 44
    • 0000417595 scopus 로고
    • Numerical methods for hyperbolic conservation laws with stiff relaxation II. Higher-order Godunov methods
    • R. B. Pember, Numerical methods for hyperbolic conservation laws with stiff relaxation II. Higher-order Godunov methods, SIAM J. Sci. Comput., 14 (1993), pp. 824-859. MR 95f:65190
    • (1993) SIAM J. Sci. Comput. , vol.14 , pp. 824-859
    • Pember, R.B.1
  • 45
    • 0039286719 scopus 로고    scopus 로고
    • R. B. Pember, Numerical methods for hyperbolic conservation laws with stiff relaxation II. Higher-order Godunov methods, SIAM J. Sci. Comput., 14 (1993), pp. 824-859. MR 95f:65190
    • MR , vol.95 F , pp. 65190
  • 46
    • 0039026206 scopus 로고    scopus 로고
    • 1 error bound for semi-implicit difference scheme applied to a stiff system of conservation laws
    • 1 error bound for semi-implicit difference scheme applied to a stiff system of conservation laws, SIAM J. Numer. Anal. 34 (1997), 1152-1166. MR 98g:65078
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 1152-1166
    • Schroll, H.J.1    Tveito, A.2    Winther, R.3
  • 47
    • 0039026206 scopus 로고    scopus 로고
    • 1 error bound for semi-implicit difference scheme applied to a stiff system of conservation laws, SIAM J. Numer. Anal. 34 (1997), 1152-1166. MR 98g:65078
    • MR , vol.98 G , pp. 65078
  • 48
    • 0030519932 scopus 로고    scopus 로고
    • Finite difference schemes for conservation laws with source terms
    • H. J. Schroll and R. Winther, Finite difference schemes for conservation laws with source terms, IMA J. Numer. Anal., 16 (1996), pp. 201-215. MR 97g:65177
    • (1996) IMA J. Numer. Anal. , vol.16 , pp. 201-215
    • Schroll, H.J.1    Winther, R.2
  • 49
    • 85120508136 scopus 로고    scopus 로고
    • H. J. Schroll and R. Winther, Finite difference schemes for conservation laws with source terms, IMA J. Numer. Anal., 16 (1996), pp. 201-215. MR 97g:65177
    • MR , vol.97 G , pp. 65177
  • 50
    • 0021513424 scopus 로고    scopus 로고
    • High resolution schemes using flux limiters for hyperbolic conservation laws
    • P. R. Sweby, High resolution schemes using flux limiters for hyperbolic conservation laws, SIAM J. Numer. Anal. 21 (1984), pp. 995-1011. MR 85m:65085
    • (1984) SIAM J. Numer. Anal. , vol.21 , pp. 995-1011
    • Sweby, P.R.1
  • 51
    • 0021513424 scopus 로고    scopus 로고
    • P. R. Sweby, High resolution schemes using flux limiters for hyperbolic conservation laws, SIAM J. Numer. Anal. 21 (1984), pp. 995-1011. MR 85m:65085
    • MR , vol.85 M , pp. 65085
  • 52
    • 84966249400 scopus 로고    scopus 로고
    • Numerical viscosity and the entropy condition for conservative difference schemes
    • E. Tadmor, Numerical viscosity and the entropy condition for conservative difference schemes, Math. Comp. 43 (1984), pp. 369-381. MR 86g:65163
    • (1984) Math. Comp. , vol.43 , pp. 369-381
    • Tadmor, E.1
  • 53
    • 84966249400 scopus 로고    scopus 로고
    • E. Tadmor, Numerical viscosity and the entropy condition for conservative difference schemes, Math. Comp. 43 (1984), pp. 369-381. MR 86g:65163
    • MR , vol.86 G , pp. 65163
  • 54
    • 0001263726 scopus 로고
    • Error bounds for fractional step methods for conservation laws with source terms
    • T. Tang and Z. H. Teng, Error bounds for fractional step methods for conservation laws with source terms, SIAM J. Numer. Anal., 32 (1995), pp. 110-127. MR 95m:65155
    • (1995) SIAM J. Numer. Anal. , vol.32 , pp. 110-127
    • Tang, T.1    Teng, Z.H.2
  • 55
    • 0039195586 scopus 로고    scopus 로고
    • T. Tang and Z. H. Teng, Error bounds for fractional step methods for conservation laws with source terms, SIAM J. Numer. Anal., 32 (1995), pp. 110-127. MR 95m:65155
    • MR , vol.95 M , pp. 65155
  • 56
    • 2442433925 scopus 로고    scopus 로고
    • Towards the ultimate conservative difference schemes V. A second order sequel to Godunov's method
    • B. Van Leer, Towards the ultimate conservative difference schemes V. A second order sequel to Godunov's method, J. Comput. Phys., 32 (1979), pp. 101-136. CMP 98:05
    • (1979) J. Comput. Phys. , vol.32 , pp. 101-136
    • Van Leer, B.1
  • 57
    • 2442433925 scopus 로고    scopus 로고
    • B. Van Leer, Towards the ultimate conservative difference schemes V. A second order sequel to Godunov's method, J. Comput. Phys., 32 (1979), pp. 101-136. CMP 98:05
    • CMP , vol.98 , pp. 05
  • 60
    • 0039787877 scopus 로고    scopus 로고
    • G. B. Whitham, Linear and nonlinear waves, J. Wiley (1974). MR 58:3905
    • MR , vol.58 , pp. 3905


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