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Volumn 357, Issue 1754, 1999, Pages 1047-1077

Self-similar numerical solutions of the porous-medium equation using moving mesh methods

Author keywords

Conservation laws; Equidistribution; Lie group invariance; Mesh adaptation; Porous medium equation; Self similar solution

Indexed keywords


EID: 0347599386     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.1999.0364     Document Type: Article
Times cited : (37)

References (14)
  • 1
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    • Scaling, self-similarity and intermediate asymptotics
    • Cambridge University Press
    • Barenblatt, G. I. 1996 Scaling, self-similarity and intermediate asymptotics. Cambridge texts in applied mathematics, vol. 14. Cambridge University Press.
    • (1996) Cambridge Texts in Applied Mathematics , vol.14
    • Barenblatt, G.I.1
  • 3
    • 0002883024 scopus 로고    scopus 로고
    • Symmetry based numerical methods for partial differential equations
    • Numerical analysis 1997 (ed. D. Griffiths, D. Higham & G. Watson), London: Longman
    • Budd, C. J. & Collins, G. J. 1998 Symmetry based numerical methods for partial differential equations. In Numerical analysis 1997 (ed. D. Griffiths, D. Higham & G. Watson), Pitman Research Notes in Mathematics Series, vol. 380, pp. 16-36, London: Longman.
    • (1998) Pitman Research Notes in Mathematics Series , vol.380 , pp. 16-36
    • Budd, C.J.1    Collins, G.J.2
  • 4
    • 0000458449 scopus 로고    scopus 로고
    • Moving mesh methods for problems with blow-up
    • Budd, C. J., Huang, W. & Russell, R. D. 1996a Moving mesh methods for problems with blow-up. SIAM J. Sci. Comp. 17, 305-327.
    • (1996) SIAM J. Sci. Comp. , vol.17 , pp. 305-327
    • Budd, C.J.1    Huang, W.2    Russell, R.D.3
  • 5
    • 0002610231 scopus 로고    scopus 로고
    • Moving mesh methods with applications to blow-up problems for PDEs
    • Numerical analysis 1995 (ed. D. Griffiths & G. Watson), London: Longman
    • Budd, C. J., Chen, J., Huang, W. & Russell, R. D. 1996b Moving mesh methods with applications to blow-up problems for PDEs. In Numerical analysis 1995 (ed. D. Griffiths & G. Watson), pp. 1-18. Pitman Research Notes in Mathematics Series, vol. 344. London: Longman.
    • (1996) Pitman Research Notes in Mathematics Series , vol.344 , pp. 1-18
    • Budd, C.J.1    Chen, J.2    Huang, W.3    Russell, R.D.4
  • 7
    • 0003362075 scopus 로고
    • Similarity solutions of nonlinear partial differential equations
    • London: Longman
    • Dresner, L. 1983 Similarity solutions of nonlinear partial differential equations. Pitman Research Notes in Mathematics Series, vol. 88. London: Longman.
    • (1983) Pitman Research Notes in Mathematics Series , vol.88
    • Dresner, L.1
  • 8
    • 0000105971 scopus 로고
    • Moving mesh methods based on moving mesh partial differential equations
    • Huang, W., Ren, Y. & Russell, R. D. 1994 Moving mesh methods based on moving mesh partial differential equations. J. Comp. Phys. 112, 279-290.
    • (1994) J. Comp. Phys. , vol.112 , pp. 279-290
    • Huang, W.1    Ren, Y.2    Russell, R.D.3
  • 9
    • 51249188354 scopus 로고
    • The asymptotic behaviour of the solution of the filtration equation
    • Kamenomostskaya, S. 1973 The asymptotic behaviour of the solution of the filtration equation. Israel J. Math. 14, 76-87.
    • (1973) Israel J. Math. , vol.14 , pp. 76-87
    • Kamenomostskaya, S.1
  • 13
    • 0005170087 scopus 로고
    • A Lyapunov functional for the evolution of solutions to the porous medium equation to self-similarity. II
    • Ralston, J. 1984 A Lyapunov functional for the evolution of solutions to the porous medium equation to self-similarity. II. J. Math. Phys. 25, 3124-3127.
    • (1984) J. Math. Phys. , vol.25 , pp. 3124-3127
    • Ralston, J.1
  • 14
    • 0000383614 scopus 로고
    • An introduction to the mathematical theory of the porous medium equation
    • (ed. M. Delfour), Dordrecht: Kluwer
    • Vazquez, J. L. 1992 An introduction to the mathematical theory of the porous medium equation. In Shape optimisation and free boundaries (ed. M. Delfour), pp. 347-389. Dordrecht: Kluwer.
    • (1992) Shape Optimisation and Free Boundaries , pp. 347-389
    • Vazquez, J.L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.