메뉴 건너뛰기




Volumn 28, Issue 3, 2006, Pages 1167-1185

Numerical methods for differential equations in random domains

Author keywords

Differential equations; Random domain; Stochastic inputs; Uncertainty quantification

Indexed keywords

COMPUTATIONAL METHODS; MEASUREMENT ERRORS; NUMERICAL METHODS; RANDOM PROCESSES; ROUGH SET THEORY; TOPOLOGY;

EID: 34249042611     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/040613160     Document Type: Article
Times cited : (171)

References (39)
  • 1
    • 0036791413 scopus 로고    scopus 로고
    • Effects of uncertainties in the domain on the solution of Neumann boundary value problems in two spatial dimensions
    • I. BABUŠKA AND J. CHLEBOUN, Effects of uncertainties in the domain on the solution of Neumann boundary value problems in two spatial dimensions., Math. Comput., 71 (2002), pp. 1339-1370.
    • (2002) Math. Comput , vol.71 , pp. 1339-1370
    • BABUŠKA, I.1    CHLEBOUN, J.2
  • 2
    • 0242473086 scopus 로고    scopus 로고
    • Effects of uncertainties in the domain on the solution of Dirichlet boundary value problems
    • I. BABUŠKA AND J. CHLEBOUN, Effects of uncertainties in the domain on the solution of Dirichlet boundary value problems, Numer. Math., 93 (2003), pp. 583-610.
    • (2003) Numer. Math , vol.93 , pp. 583-610
    • BABUŠKA, I.1    CHLEBOUN, J.2
  • 3
    • 13844319204 scopus 로고    scopus 로고
    • Galerkin finite element approximations of stochastic elliptic differential equations
    • I. BABUŠKA, R. TEMPONE, AND G. E. ZOURARIS, Galerkin finite element approximations of stochastic elliptic differential equations, SIAM J. Numer. Anal., 42 (2004), pp. 800-825.
    • (2004) SIAM J. Numer. Anal , vol.42 , pp. 800-825
    • BABUŠKA, I.1    TEMPONE, R.2    ZOURARIS, G.E.3
  • 4
    • 0016626491 scopus 로고
    • Application de la mèthode des èlèments finis à l'approximation d'un problème de domaine optimal. Mèthode de rèsolution des problèmes approchès
    • D. BEGIS AND R. GLOWINSKI, Application de la mèthode des èlèments finis à l'approximation d'un problème de domaine optimal. Mèthode de rèsolution des problèmes approchès, Appl. Math. Optim., 2 (1975), pp. 130-169.
    • (1975) Appl. Math. Optim , vol.2 , pp. 130-169
    • BEGIS, D.1    GLOWINSKI, R.2
  • 6
    • 0037397032 scopus 로고    scopus 로고
    • Heat conduction across irregular and fractal-like surfaces
    • M. BLYTH AND C. POZRIKIDIS, Heat conduction across irregular and fractal-like surfaces., Int. J. Heat Mass Transf., 46 (2003), pp. 1329-1339.
    • (2003) Int. J. Heat Mass Transf , vol.46 , pp. 1329-1339
    • BLYTH, M.1    POZRIKIDIS, C.2
  • 7
    • 0000561497 scopus 로고
    • Diffusive transport across irregular and fractal walls
    • M. BRADY AND C. POZRIKIDIS, Diffusive transport across irregular and fractal walls., Proc. R. Soc. Lond. A Math. Phys. Sci., 442 (1993), pp. 571-583.
    • (1993) Proc. R. Soc. Lond. A Math. Phys. Sci , vol.442 , pp. 571-583
    • BRADY, M.1    POZRIKIDIS, C.2
  • 8
    • 4544321108 scopus 로고    scopus 로고
    • Fractal properties of equipotentials close to a rough conducting surface
    • D. CAJUEIRO, V. SAMPAIO, C. DE CASTILHO, AND R. ANDRADE, Fractal properties of equipotentials close to a rough conducting surface, J. Phys. Condensed Matter, 11 (1999), pp. 4985-4992.
    • (1999) J. Phys. Condensed Matter , vol.11 , pp. 4985-4992
    • CAJUEIRO, D.1    SAMPAIO, V.2    DE CASTILHO, C.3    ANDRADE, R.4
  • 9
    • 0035964634 scopus 로고    scopus 로고
    • Solution of stochastic partial differential equations using Galerkin finite element techniques
    • M. DEB, I. BABUŠKA, AND J. ODEN, Solution of stochastic partial differential equations using Galerkin finite element techniques, Comput. Methods Appl. Mech. Engrg., 190 (2001), pp. 6359-6372.
    • (2001) Comput. Methods Appl. Mech. Engrg , vol.190 , pp. 6359-6372
    • DEB, M.1    BABUŠKA, I.2    ODEN, J.3
  • 10
    • 0000611914 scopus 로고
    • Harmonic measure around a linearly self-similar tree
    • C. EVERTSZ AND B. MANDELBROT, Harmonic measure around a linearly self-similar tree, J. Phys. A, 25 (1992), pp. 1781-1797.
    • (1992) J. Phys. A , vol.25 , pp. 1781-1797
    • EVERTSZ, C.1    MANDELBROT, B.2
  • 12
    • 10444261986 scopus 로고    scopus 로고
    • Finite elements for elliptic problems with stochastic coefficients
    • P. FRAUENFELDER, C. SCHWAB, AND R. TODOR, Finite elements for elliptic problems with stochastic coefficients, Comput. Methods Appl. Mech. Engrg., 194 (2005), pp. 205-228.
    • (2005) Comput. Methods Appl. Mech. Engrg , vol.194 , pp. 205-228
    • FRAUENFELDER, P.1    SCHWAB, C.2    TODOR, R.3
  • 13
    • 0035916793 scopus 로고    scopus 로고
    • Conductive heat transport across rough surfaces and interfaces between two conforming media
    • M. FYRILLAS AND C. POZRIKIDIS, Conductive heat transport across rough surfaces and interfaces between two conforming media, Int. J. Heat Mass Transf., 44 (2001), pp. 1789-1801.
    • (2001) Int. J. Heat Mass Transf , vol.44 , pp. 1789-1801
    • FYRILLAS, M.1    POZRIKIDIS, C.2
  • 15
    • 0000827365 scopus 로고
    • Contact of nominally flat surfaces
    • J. GREENWOOD AND J. WILLIAMSON, Contact of nominally flat surfaces, Proc. Roy. Soc. A, 295 (1966), pp. 300-319.
    • (1966) Proc. Roy. Soc. A , vol.295 , pp. 300-319
    • GREENWOOD, J.1    WILLIAMSON, J.2
  • 16
    • 0003113147 scopus 로고    scopus 로고
    • Simulation of stationary non-Gaussian translation processes
    • M. GRIGORIU, Simulation of stationary non-Gaussian translation processes, J. Eng. Mech., 124 (1998), pp. 121-126.
    • (1998) J. Eng. Mech , vol.124 , pp. 121-126
    • GRIGORIU, M.1
  • 17
    • 0020766935 scopus 로고
    • Effects of local field variations on the contrast of a field-ion microscope
    • H. HOMEIER AND D. KINGHAM, Effects of local field variations on the contrast of a field-ion microscope, J. Phys. D, 16 (1983), pp. L115-L120.
    • (1983) J. Phys. D , vol.16
    • HOMEIER, H.1    KINGHAM, D.2
  • 19
    • 14644396217 scopus 로고    scopus 로고
    • Interface dynamics in randomly heterogeneous porous media
    • Y. N. LAZAREV, P. V. PETROV, AND D. M. TARTAKOVSKY, Interface dynamics in randomly heterogeneous porous media, Adv. Water Resour., 28 (2005), pp. 393-403.
    • (2005) Adv. Water Resour , vol.28 , pp. 393-403
    • LAZAREV, Y.N.1    PETROV, P.V.2    TARTAKOVSKY, D.M.3
  • 20
    • 2942555049 scopus 로고    scopus 로고
    • Uncertainty propagation using Wiener-Haar expansions
    • O. LE MAITRE, O. KNIO, H. NAJM, AND R. GHANEM, Uncertainty propagation using Wiener-Haar expansions, J. Comput. Phys., 197 (2004), pp. 28-57.
    • (2004) J. Comput. Phys , vol.197 , pp. 28-57
    • LE MAITRE, O.1    KNIO, O.2    NAJM, H.3    GHANEM, R.4
  • 21
    • 3242712896 scopus 로고    scopus 로고
    • Multi-resolution analysis of Wiener-type uncertainty propagation schemes
    • O. LE MAITRE, H. NAJM, R. GHANEM, AND O. KNIO, Multi-resolution analysis of Wiener-type uncertainty propagation schemes, J. Comput. Phys., 197 (2004), pp. 502-531.
    • (2004) J. Comput. Phys , vol.197 , pp. 502-531
    • LE MAITRE, O.1    NAJM, H.2    GHANEM, R.3    KNIO, O.4
  • 22
    • 0022719849 scopus 로고
    • Probabilistic finite elements for nonlinear structural dynamics
    • W. LIU, T. BELYTSCHKO, AND A. MANI, Probabilistic finite elements for nonlinear structural dynamics, Comput. Methods Appl. Mech. Engrg., 56 (1986), pp. 61-81.
    • (1986) Comput. Methods Appl. Mech. Engrg , vol.56 , pp. 61-81
    • LIU, W.1    BELYTSCHKO, T.2    MANI, A.3
  • 23
    • 0003981320 scopus 로고
    • 4th ed, Springer-Verlag, New York, Berlin
    • M. LOÈVE, Probability Theory, 4th ed., Springer-Verlag, New York, Berlin, 1977.
    • (1977) Probability Theory
    • LOÈVE, M.1
  • 25
    • 34249070021 scopus 로고    scopus 로고
    • B. ØKSENDAL, Stochastic Differential Equations. An Introduction with Applications, 5th ed., Springer-Verlag, Berlin, 1998.
    • B. ØKSENDAL, Stochastic Differential Equations. An Introduction with Applications, 5th ed., Springer-Verlag, Berlin, 1998.
  • 26
    • 0346112464 scopus 로고
    • A model for the boundary condition of a porous material, Part 2
    • S. RICHARDSON, A model for the boundary condition of a porous material, Part 2, J. Fluid Mech., 49 (1971), pp. 327-336.
    • (1971) J. Fluid Mech , vol.49 , pp. 327-336
    • RICHARDSON, S.1
  • 28
    • 0036532174 scopus 로고    scopus 로고
    • Simulation of multi-dimensional non-Gaussian non-stationary random fields
    • S. SAKAMOTO AND R. GHANEM, Simulation of multi-dimensional non-Gaussian non-stationary random fields, Prob. Eng. Mech., 17 (2002), pp. 167-176.
    • (2002) Prob. Eng. Mech , vol.17 , pp. 167-176
    • SAKAMOTO, S.1    GHANEM, R.2
  • 29
    • 35949007598 scopus 로고
    • Gradients of potential fields on rough surfaces: Perturbative calculation of the singularity distribution function f(α) for small surface dimension
    • K. SARKAR AND C. MENEVEAU, Gradients of potential fields on rough surfaces: Perturbative calculation of the singularity distribution function f(α) for small surface dimension, Phys. Rev. E, 47 (1993), pp. 95-966.
    • (1993) Phys. Rev. E , vol.47 , pp. 95-966
    • SARKAR, K.1    MENEVEAU, C.2
  • 30
    • 84861979006 scopus 로고
    • Simulation of stochastic processes by spectral representations
    • M. SHINOZUKA AND G. DEODATIS, Simulation of stochastic processes by spectral representations, Appl. Mech. Rev., 44 (1991), pp. 191-203.
    • (1991) Appl. Mech. Rev , vol.44 , pp. 191-203
    • SHINOZUKA, M.1    DEODATIS, G.2
  • 31
    • 16244409214 scopus 로고    scopus 로고
    • Physical systems with random uncertainties: Chaos representations with arbitrary probability measure
    • C. SOIZE AND R. GHANEM, Physical systems with random uncertainties: Chaos representations with arbitrary probability measure, SIAM. J. Sci. Comput., 26 (2004), pp. 395-410.
    • (2004) SIAM. J. Sci. Comput , vol.26 , pp. 395-410
    • SOIZE, C.1    GHANEM, R.2
  • 32
    • 84956071306 scopus 로고
    • A model for the boundary condition of a porous material, Part 1
    • G. TAYLOR, A model for the boundary condition of a porous material, Part 1, J. Fluid Mech., 49 (1971), pp. 319-326.
    • (1971) J. Fluid Mech , vol.49 , pp. 319-326
    • TAYLOR, G.1
  • 34
    • 0023591830 scopus 로고
    • Transport processes along fractals. The Cantor-Taylor brush, Physicochem
    • M. VIGNES-ADLER, P. ADLER, AND P. GOUGAT, Transport processes along fractals. The Cantor-Taylor brush, Physicochem. Hydrodynam., 8 (1987), pp. 401-422.
    • (1987) Hydrodynam , vol.8 , pp. 401-422
    • VIGNES-ADLER, M.1    ADLER, P.2    GOUGAT, P.3
  • 37
    • 0037249229 scopus 로고    scopus 로고
    • The Wiener-Askey polynomial chaos for stochastic differential equations
    • D. XIU AND G. E. KARNIADAKIS, The Wiener-Askey polynomial chaos for stochastic differential equations, SIAM J. Sci. Comput., 24 (2002), pp. 619-644.
    • (2002) SIAM J. Sci. Comput , vol.24 , pp. 619-644
    • XIU, D.1    KARNIADAKIS, G.E.2
  • 38
    • 0037408312 scopus 로고    scopus 로고
    • Modeling uncertainty in flow simulations via generalized polynomial chaos
    • D. XIU AND G. E. KARNIADAKIS, Modeling uncertainty in flow simulations via generalized polynomial chaos, J. Comput. Phys., 187 (2003), pp. 137-167.
    • (2003) J. Comput. Phys , vol.187 , pp. 137-167
    • XIU, D.1    KARNIADAKIS, G.E.2
  • 39
    • 0024048378 scopus 로고
    • Digital generation of non-Gaussian stochastic fields
    • F. YAMAZAKI AND M. SHINOZUKA, Digital generation of non-Gaussian stochastic fields, J. Eng. Mech., 114 (1988), pp. 1183-1197.
    • (1988) J. Eng. Mech , vol.114 , pp. 1183-1197
    • YAMAZAKI, F.1    SHINOZUKA, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.