메뉴 건너뛰기




Volumn 28, Issue 4, 2010, Pages 474-488

Convergence rates for difference schemes for polyhedral nonlinear parabolic equations

Author keywords

Convergence rate; Error estimates; Finite difference schemes; Viscosity solutions

Indexed keywords


EID: 77955312746     PISSN: 02549409     EISSN: None     Source Type: Journal    
DOI: 10.4208/jcm.1003-m0013     Document Type: Article
Times cited : (4)

References (18)
  • 1
    • 38849122631 scopus 로고    scopus 로고
    • Error bounds for monotone approximation schemes for parabolic Hamilton-Jacobi-Bellman equations
    • G. Barles and E. R. Jakobsen, Error bounds for monotone approximation schemes for parabolic Hamilton-Jacobi-Bellman equations, Math. Comput., 76: 260 (2007), 1861-1893 (electronic).
    • (2007) Math. Comput. , vol.76 , Issue.260 , pp. 1861-1893
    • Barles, G.1    Jakobsen, E.R.2
  • 2
    • 84974753170 scopus 로고    scopus 로고
    • Convergence of approximation schemes for fully nonlinear second order equations
    • G. Barles and P. E. Souganidis, Convergence of approximation schemes for fully nonlinear second order equations, Asymptotic Anal., 4: 3 (1999), 271-283.
    • (1999) Asymptotic Anal , vol.4 , Issue.3 , pp. 271-283
    • Barles, G.1    Souganidis, P.E.2
  • 3
    • 0038269843 scopus 로고    scopus 로고
    • 2,α regularity theory for a class of nonconvex fully nonlinear elliptic equations
    • 2,α regularity theory for a class of nonconvex fully nonlinear elliptic equations, J. Math. Pure. Appl. (9), 82: 5 (2003), 573-612.
    • (2003) J. Math. Pure. Appl. , vol.82 , Issue.9 , pp. 573-612
    • Cabre, X.1    Caffarelli, L.A.2
  • 5
    • 37649004216 scopus 로고    scopus 로고
    • A rate of convergence for monotone finite difference approximations to fully nonlinear, uniformly elliptic PDEs
    • L. A. Caffarelli and P. E. Souganidis, A rate of convergence for monotone finite difference approximations to fully nonlinear, uniformly elliptic PDEs, Commun. Pur. Appl. Math., 61: 1 (2008), 1-17.
    • (2008) Commun. Pur. Appl. Math. , vol.61 , Issue.1 , pp. 1-17
    • Caffarelli, L.A.1    Souganidis, P.E.2
  • 6
    • 0001162786 scopus 로고
    • On the partial difference equations of mathematical physics
    • R. Courant, K. O. Friedrichs, and H. Lewy, On the partial difference equations of mathematical physics, IBM J. Res. Dev., 11 (1967), 215-234.
    • (1967) IBM J. Res. Dev , vol.11 , pp. 215-234
    • Courant, R.1    Friedrichs, K.O.2    Lewy, H.3
  • 7
    • 84967708673 scopus 로고
    • User's guide to viscosity solutions of second order partial differential equations
    • M. G. Crandall, H. Ishii, and P.-L. Lions, User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. (N.S.), 27: 1 (1992), 1-67.
    • (1992) Bull. Amer. Math. Soc. (N.S.) , vol.27 , Issue.1 , pp. 1-67
    • Crandall, M.G.1    Ishii, H.2    Lions, P.-L.3
  • 8
    • 34547457979 scopus 로고    scopus 로고
    • The rate of convergence of finite-difference approximations for parabolic Bellman equations with Lipschitz coefficients in cylindrical domains
    • H. Dong and N. V. Krylov, The rate of convergence of finite-difference approximations for parabolic Bellman equations with Lipschitz coefficients in cylindrical domains, Appl. Math. Opt., 56: 1 (2007), 37-66.
    • (2007) Appl. Math. Opt. , vol.56 , Issue.1 , pp. 37-66
    • Dong, H.1    Krylov, N.V.2
  • 9
    • 84990553687 scopus 로고
    • Classical solutions of fully nonlinear, convex, second-order elliptic equations
    • L. C. Evans, Classical solutions of fully nonlinear, convex, second-order elliptic equations, Commun. Pur. Appl. Math., 35: 3 (1982), 333-363.
    • (1982) Commun. Pur. Appl. Math. , vol.35 , Issue.3 , pp. 333-363
    • Evans, L.C.1
  • 11
    • 0007455893 scopus 로고    scopus 로고
    • On the rate of convergence of finite-difference approximations for Bellman's equations
    • N. V. Krylov, On the rate of convergence of finite-difference approximations for Bellman's equations, Algebra i Analiz, 9: 3 (1997), 245-256.
    • (1997) Algebra i Analiz , vol.9 , Issue.3 , pp. 245-256
    • Krylov, N.V.1
  • 12
    • 0040457644 scopus 로고
    • On the discrete maximum principle for parabolic difference operators
    • H.-J. Kuo and N. S. Trudinger, On the discrete maximum principle for parabolic difference operators, RAIRO Model. Math. Anal. Numer., 27: 6 (1993), 719-737.
    • (1993) RAIRO Model. Math. Anal. Numer. , vol.27 , Issue.6 , pp. 719-737
    • Kuo, H.-J.1    Trudinger, N.S.2
  • 13
    • 11944255628 scopus 로고    scopus 로고
    • A convergent monotone difference scheme for motion of level sets by mean curvature
    • A. M. Oberman, A convergent monotone difference scheme for motion of level sets by mean curvature, Numer. Math., 99: 2 (2004), 365-379.
    • (2004) Numer. Math. , vol.99 , Issue.2 , pp. 365-379
    • Oberman, A.M.1
  • 14
    • 21644465169 scopus 로고    scopus 로고
    • A convergent difference scheme for the infinity Laplacian: construction of absolutely minimizing Lipschitz extensions
    • A. M. Oberman, A convergent difference scheme for the infinity Laplacian: construction of absolutely minimizing Lipschitz extensions, Math. Compute., 74: 251 (2005), 1217-1230 (electronic).
    • (2005) Math. Compute. , vol.74 , Issue.251 , pp. 1217-1230
    • Oberman, A.M.1
  • 15
    • 34247269678 scopus 로고    scopus 로고
    • Convergent difference schemes for degenerate elliptic and parabolic equations: Hamilton-Jacobi equations and free boundary problems
    • A. M. Oberman, Convergent difference schemes for degenerate elliptic and parabolic equations: Hamilton-Jacobi equations and free boundary problems, SIAM J. Number. Anal, 44: 2 (2006), 879-895 (electronic).
    • (2006) SIAM J. Number. Anal , vol.44 , Issue.2 , pp. 879-895
    • Oberman, A.M.1
  • 16
    • 47249122195 scopus 로고    scopus 로고
    • Wide stencil finite difference schemes for the elliptic Monge-Ampere equation and functions of the eigenvalues of the Hessian
    • A. M. Oberman, Wide stencil finite difference schemes for the elliptic Monge-Ampere equation and functions of the eigenvalues of the Hessian, Discrete Cont. Dyn-B, 10: 1 (2008), 221-238.
    • (2008) Discrete Cont. Dyn-B , vol.10 , Issue.1 , pp. 221-238
    • Oberman, A.M.1
  • 17
    • 84968512228 scopus 로고
    • On the regularity theory of fully nonlinear parabolic equations
    • L.-H. Wang, On the regularity theory of fully nonlinear parabolic equations, Bull. Amer. Math. Soc. (N.S.), 22: 1 (1990), 107-114.
    • (1990) Bull. Amer. Math. Soc. (N.S.) , vol.22 , Issue.1 , pp. 107-114
    • Wang, L.-H.1
  • 18
    • 84990616983 scopus 로고
    • On the regularity theory of fully nonlinear parabolic equations. I
    • L.-H. Wang, On the regularity theory of fully nonlinear parabolic equations. I, Commun. Pur. Appl. Math., 45: 1 (1992), 27-76.
    • (1992) Commun. Pur. Appl. Math. , vol.45 , Issue.1 , pp. 27-76
    • Wang, L.-H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.