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Volumn 61, Issue 2, 2011, Pages 170-180

MLPG method for two-dimensional diffusion equation with Neumann's and non-classical boundary conditions

Author keywords

Finite differences; Heat equation; MLPG method; Neumann's boundary conditions; Non classical integral boundary condition; Parabolic partial differential equations

Indexed keywords

FINITE DIFFERENCE; HEAT EQUATION; INTEGRAL BOUNDARY CONDITIONS; MLPG METHOD; NEUMANN'S BOUNDARY CONDITION; PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS;

EID: 78649668752     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2010.09.002     Document Type: Article
Times cited : (69)

References (40)
  • 1
    • 0043132011 scopus 로고    scopus 로고
    • A modified element-free Galerkin method with essential boundary conditions enforced by an extended partition of unity finite element weight function
    • M.K. Alves, and R. Rossi A modified element-free Galerkin method with essential boundary conditions enforced by an extended partition of unity finite element weight function Internat. J. Numer. Methods Engrg. 57 2003 1523 1552
    • (2003) Internat. J. Numer. Methods Engrg. , vol.57 , pp. 1523-1552
    • Alves, M.K.1    Rossi, R.2
  • 4
    • 0042964833 scopus 로고    scopus 로고
    • The meshless local Petrov-Galerkin (MLPG) method: A simple and less costly alternative to the finite element and boundary element methods
    • S.N. Atluri, and S. Shen The meshless local Petrov-Galerkin (MLPG) method: a simple and less costly alternative to the finite element and boundary element methods Comput. Modeling Engrg. Sci. 3 2002 11 51
    • (2002) Comput. Modeling Engrg. Sci. , vol.3 , pp. 11-51
    • Atluri, S.N.1    Shen, S.2
  • 5
    • 0032136132 scopus 로고    scopus 로고
    • A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics
    • S.N. Atluri, and T.L. Zhu A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics Comput. Mech. 22 1998 117 127
    • (1998) Comput. Mech. , vol.22 , pp. 117-127
    • Atluri, S.N.1    Zhu, T.L.2
  • 6
    • 0001022815 scopus 로고    scopus 로고
    • A new meshless local Petrov-Galerkin (MLPG) approach to nonlinear problems in computer modeling and simulation
    • S.N. Atluri, and T.L. Zhu A new meshless local Petrov-Galerkin (MLPG) approach to nonlinear problems in computer modeling and simulation Comput. Modeling Simulation Engrg. 3 1998 187 196
    • (1998) Comput. Modeling Simulation Engrg. , vol.3 , pp. 187-196
    • Atluri, S.N.1    Zhu, T.L.2
  • 7
    • 36949023617 scopus 로고    scopus 로고
    • Free and forced vibrations of a segmented bar by a meshless local Petrov-Galerkin (MLPG) formulation
    • R.C. Batra, M. Porfiri, and D. Spinello Free and forced vibrations of a segmented bar by a meshless local Petrov-Galerkin (MLPG) formulation Comput. Mech. 41 2008 473 491
    • (2008) Comput. Mech. , vol.41 , pp. 473-491
    • Batra, R.C.1    Porfiri, M.2    Spinello, D.3
  • 8
    • 0000009156 scopus 로고
    • An inverse problem of finding a parameter in a semi-linear heat equation
    • J.R. Cannon, and Y. Lin An inverse problem of finding a parameter in a semi-linear heat equation J. Math. Anal. Appl. 145 2 1990 470 484
    • (1990) J. Math. Anal. Appl. , vol.145 , Issue.2 , pp. 470-484
    • Cannon, J.R.1    Lin, Y.2
  • 9
    • 84948498782 scopus 로고
    • The solution of the diffusion equation in two-space variables subject to the specification of mass
    • J.R. Cannon, Y. Lin, and A.L. Matheson The solution of the diffusion equation in two-space variables subject to the specification of mass Appl. Anal. 50 1993 1 19
    • (1993) Appl. Anal. , vol.50 , pp. 1-19
    • Cannon, J.R.1    Lin, Y.2    Matheson, A.L.3
  • 10
    • 0022709536 scopus 로고
    • Diffusion subject to specification of mass
    • J.R. Cannon, and J. van der Hoek Diffusion subject to specification of mass J. Math. Anal. Appl. 115 1986 517 529
    • (1986) J. Math. Anal. Appl. , vol.115 , pp. 517-529
    • Cannon, J.R.1    Van Der Hoek, J.2
  • 11
    • 0001295415 scopus 로고
    • A reaction-diffusion system arising in modeling man-environment diseases
    • V. Capsso, and K. Kunisch A reaction-diffusion system arising in modeling man-environment diseases Quart. Appl. Math. 46 1988 431 449
    • (1988) Quart. Appl. Math. , vol.46 , pp. 431-449
    • Capsso, V.1    Kunisch, K.2
  • 12
    • 0141792683 scopus 로고    scopus 로고
    • A coupled finite element and meshless local Petrov-Galerkin method for two-dimensional potential problems
    • T. Chen, and I.S. Raju A coupled finite element and meshless local Petrov-Galerkin method for two-dimensional potential problems Comput. Methods Appl. Mech. Engrg. 192 2003 4533 4550
    • (2003) Comput. Methods Appl. Mech. Engrg. , vol.192 , pp. 4533-4550
    • Chen, T.1    Raju, I.S.2
  • 13
    • 42949093085 scopus 로고    scopus 로고
    • Error estimates for the finite point method
    • Rongjun Cheng, and Yumin Cheng Error estimates for the finite point method Appl. Numer. Math. 58 2008 884 898
    • (2008) Appl. Numer. Math. , vol.58 , pp. 884-898
    • Cheng, R.1    Cheng, Y.2
  • 14
    • 0001265252 scopus 로고
    • A parabolic equation with nonlocal boundary conditions arising from electrochemistry
    • Y.S. Choi, and K.Y. Chan A parabolic equation with nonlocal boundary conditions arising from electrochemistry Nonlinear Anal. Theory Methods Appl. 18 4 1992 317 331
    • (1992) Nonlinear Anal. Theory Methods Appl. , vol.18 , Issue.4 , pp. 317-331
    • Choi, Y.S.1    Chan, K.Y.2
  • 15
    • 0000355020 scopus 로고
    • Existence of a property of solutions of the heat equation subject to linear thermoelasticity and other theories
    • W.A. Day Existence of a property of solutions of the heat equation subject to linear thermoelasticity and other theories Quart. Appl. Math. 40 1982 319 330
    • (1982) Quart. Appl. Math. , vol.40 , pp. 319-330
    • Day, W.A.1
  • 16
    • 0020544005 scopus 로고
    • A decreasing property of solutions of a parabolic equation with applications to thermoelasticity and other theories
    • W.A. Day A decreasing property of solutions of a parabolic equation with applications to thermoelasticity and other theories Quart. Appl. Math. XLIV 1983 468 475
    • (1983) Quart. Appl. Math. , vol.44 , pp. 468-475
    • Day, W.A.1
  • 17
    • 0036148474 scopus 로고    scopus 로고
    • Second-order schemes for a boundary value problem with Neumann's boundary conditions
    • M. Dehghan Second-order schemes for a boundary value problem with Neumann's boundary conditions J. Comput. Appl. Math. 138 2002 173 184
    • (2002) J. Comput. Appl. Math. , vol.138 , pp. 173-184
    • Dehghan, M.1
  • 18
    • 61549088742 scopus 로고    scopus 로고
    • Meshless Local Petrov-Galerkin (MLPG) method for the unsteady magnetohydrodynamic (MHD) flow through pipe with arbitrary wall conductivity
    • M. Dehghan, and D. Mirzaei Meshless Local Petrov-Galerkin (MLPG) method for the unsteady magnetohydrodynamic (MHD) flow through pipe with arbitrary wall conductivity Appl. Numer. Math. 59 2009 1043 1058
    • (2009) Appl. Numer. Math. , vol.59 , pp. 1043-1058
    • Dehghan, M.1    Mirzaei, D.2
  • 19
    • 0001683045 scopus 로고
    • The reformulation and numerical solution of certain nonclassical initial-boundary value problems
    • G. Fairweather, and R.D. Saylor The reformulation and numerical solution of certain nonclassical initial-boundary value problems SIAM J. Sci. Statist. Comput. 12 1991 127 144
    • (1991) SIAM J. Sci. Statist. Comput. , vol.12 , pp. 127-144
    • Fairweather, G.1    Saylor, R.D.2
  • 20
    • 0007905879 scopus 로고
    • An inverse problem for a class of quasilinear parabolic equations
    • Y. Lin An inverse problem for a class of quasilinear parabolic equations SIAM J. Math. Anal. 22 1991 146 156
    • (1991) SIAM J. Math. Anal. , vol.22 , pp. 146-156
    • Lin, Y.1
  • 21
    • 35348827306 scopus 로고    scopus 로고
    • A comparison of numerical integration rules for the meshless local Petrov-Galerkin method
    • A. Mazzia, M. Ferronato, G. Pini, and G. Gambolati A comparison of numerical integration rules for the meshless local Petrov-Galerkin method Numer. Algorithms 45 2007 61 74
    • (2007) Numer. Algorithms , vol.45 , pp. 61-74
    • Mazzia, A.1    Ferronato, M.2    Pini, G.3    Gambolati, G.4
  • 22
    • 73449115631 scopus 로고    scopus 로고
    • Meshless local Petrov-Galerkin (MLPG) approximation to the two dimensional sine-Gordon equation
    • D. Mirzaei, and M. Dehghan Meshless local Petrov-Galerkin (MLPG) approximation to the two dimensional sine-Gordon equation J. Comput. Appl. Math. 233 2010 2737 2754
    • (2010) J. Comput. Appl. Math. , vol.233 , pp. 2737-2754
    • Mirzaei, D.1    Dehghan, M.2
  • 23
    • 77949295595 scopus 로고    scopus 로고
    • A meshless based method for solution of integral equations
    • D. Mirzaei, and M. Dehghan A meshless based method for solution of integral equations Appl. Numer. Math. 60 2010 245 262
    • (2010) Appl. Numer. Math. , vol.60 , pp. 245-262
    • Mirzaei, D.1    Dehghan, M.2
  • 25
    • 14844327509 scopus 로고    scopus 로고
    • Three-dimensional transient heat conduction in a functionally graded thick plate with a higher-order plate theory and a meshless local Petrov-Galerkin method
    • L.F. Qian, and R.C. Batra Three-dimensional transient heat conduction in a functionally graded thick plate with a higher-order plate theory and a meshless local Petrov-Galerkin method Comput. Mech. 35 2005 214 226
    • (2005) Comput. Mech. , vol.35 , pp. 214-226
    • Qian, L.F.1    Batra, R.C.2
  • 26
    • 8344270336 scopus 로고    scopus 로고
    • Meshless local Petrov-Galerkin method for heat conduction problem in an anisotropic medium
    • J. Sladek, V. Sladek, and S.N. Atluri Meshless local Petrov-Galerkin method for heat conduction problem in an anisotropic medium CMES Comput. Model. Eng. Sci. 6 2004 309 318
    • (2004) CMES Comput. Model. Eng. Sci. , vol.6 , pp. 309-318
    • Sladek, J.1    Sladek, V.2    Atluri, S.N.3
  • 27
    • 37849187035 scopus 로고    scopus 로고
    • Heat conduction analysis of 3D axisymmetric and anisotropic FGM bodies by meshless local Petrov-Galerkin method
    • J. Sladek, V. Sladek, Ch. Hellmich, and J. Eberhardsteiner Heat conduction analysis of 3D axisymmetric and anisotropic FGM bodies by meshless local Petrov-Galerkin method Comput. Mech. 39 2007 323 333
    • (2007) Comput. Mech. , vol.39 , pp. 323-333
    • Sladek, J.1    Sladek, V.2    Hellmich, C.3    Eberhardsteiner, J.4
  • 28
    • 1242343855 scopus 로고    scopus 로고
    • Local BIEM for transient heat conduction analysis in 3-D axisymmetric functionally graded solids
    • J. Sladek, V. Sladek, J. Krivacek, and Ch. Zhang Local BIEM for transient heat conduction analysis in 3-D axisymmetric functionally graded solids Comput. Mech. 32 2003 169 176
    • (2003) Comput. Mech. , vol.32 , pp. 169-176
    • Sladek, J.1    Sladek, V.2    Krivacek, J.3    Zhang, Ch.4
  • 29
    • 56849098587 scopus 로고    scopus 로고
    • Analysis of transient heat conduction in 3D anisotropic functionally graded solids by the MLPG
    • J. Sladek, V. Sladek, C.L. Tan, and S.N. Atluri Analysis of transient heat conduction in 3D anisotropic functionally graded solids by the MLPG Comput. Modeling Engrg. Sci. 32 2008 161 174
    • (2008) Comput. Modeling Engrg. Sci. , vol.32 , pp. 161-174
    • Sladek, J.1    Sladek, V.2    Tan, C.L.3    Atluri, S.N.4
  • 30
    • 27744461613 scopus 로고    scopus 로고
    • Transient heat conduction in anisotropic and functionally graded media by local integral equations
    • V. Sladek, J. Sladek, M. Tanaka, and Ch. Zhang Transient heat conduction in anisotropic and functionally graded media by local integral equations Engrg. Anal. Bound. Elem. 29 2005 1047 1065
    • (2005) Engrg. Anal. Bound. Elem. , vol.29 , pp. 1047-1065
    • Sladek, V.1    Sladek, J.2    Tanaka, M.3    Zhang, Ch.4
  • 31
    • 67349167645 scopus 로고    scopus 로고
    • Inverse fracture problems in piezoelectric solids by local integral equation method
    • J. Sladek, V. Sladek, P.H. Wen, and Y.C. Hon Inverse fracture problems in piezoelectric solids by local integral equation method Engrg. Anal. Bound. Elem. 33 2009 1089 1099
    • (2009) Engrg. Anal. Bound. Elem. , vol.33 , pp. 1089-1099
    • Sladek, J.1    Sladek, V.2    Wen, P.H.3    Hon, Y.C.4
  • 32
    • 0142217203 scopus 로고    scopus 로고
    • Transient heat conduction analysis in functionally graded materials by the meshless local boundary integral equation method
    • J. Sladek, V. Sladek, and Ch. Zhang Transient heat conduction analysis in functionally graded materials by the meshless local boundary integral equation method Comput. Mater. Sci. 28 2003 494 504
    • (2003) Comput. Mater. Sci. , vol.28 , pp. 494-504
    • Sladek, J.1    Sladek, V.2    Zhang, Ch.3
  • 33
    • 28244471571 scopus 로고    scopus 로고
    • Meshless local Petrov-Galerkin method for continuously nonhomogeneous linear viscoelastic solids
    • DOI 10.1007/s00466-005-0715-0
    • J. Sladek, V. Sladek, Ch. Zhang, and M. Schanz Meshless local Petrov-Galerkin method for continuously nonhomogeneous linear viscoelastic solids Comput. Mech. 37 2006 279 289 (Pubitemid 41705527)
    • (2006) Computational Mechanics , vol.37 , Issue.3 , pp. 279-289
    • Sladek, J.1    Sladek, V.2    Zhang, Ch.3    Schanz, M.4
  • 34
    • 42149184844 scopus 로고    scopus 로고
    • A MLPG (LBIE) numerical method for solving 2D incompressible and nearly incompressible elastostatic problems
    • V. Vavourakis, and D. Polyzos A MLPG (LBIE) numerical method for solving 2D incompressible and nearly incompressible elastostatic problems Comm. Numer. Methods Engrg. 24 2008 281 296
    • (2008) Comm. Numer. Methods Engrg. , vol.24 , pp. 281-296
    • Vavourakis, V.1    Polyzos, D.2
  • 35
    • 0025230129 scopus 로고
    • The numerical method for the conduction subject to moving boundary energy specification
    • S. Wang The numerical method for the conduction subject to moving boundary energy specification Numer. Heat Transfer 130 1990 35 38
    • (1990) Numer. Heat Transfer , vol.130 , pp. 35-38
    • Wang, S.1
  • 36
    • 34248229743 scopus 로고    scopus 로고
    • Analysis of microelectromechanical systems (mems) devices by the meshless point weighted least-squares method
    • Q.X. Wang, H. Li, and K.Y. Lam Analysis of microelectromechanical systems (mems) devices by the meshless point weighted least-squares method Comput. Mech. 40 2007 1 11
    • (2007) Comput. Mech. , vol.40 , pp. 1-11
    • Wang, Q.X.1    Li, H.2    Lam, K.Y.3
  • 37
    • 0003017084 scopus 로고
    • A finite difference solution to an inverse problem determining a control function in a parabolic partial differential equations
    • S. Wang, and Y. Lin A finite difference solution to an inverse problem determining a control function in a parabolic partial differential equations Inverse Problems 5 1989 631 640
    • (1989) Inverse Problems , vol.5 , pp. 631-640
    • Wang, S.1    Lin, Y.2
  • 38
    • 0025068163 scopus 로고
    • Numerical method for the diffusion equation with nonlocal boundary specifications
    • DOI 10.1016/0020-7225(90)90056-O
    • S. Wang, and Y. Lin A numerical method for the diffusion equation with nonlocal boundary specifications Internat. J. Engrg. Sci. 28 1990 543 546 (Pubitemid 20735815)
    • (1990) International Journal of Engineering Science , vol.28 , Issue.6 , pp. 543-546
    • Wang Shingmin1    Lin Yanping2
  • 39
    • 0141460846 scopus 로고    scopus 로고
    • Error estimates for moving least square approximations
    • C. Zuppa Error estimates for moving least square approximations Bull. Braz. Math. Soc. (N.S.) 34 2003 231 249
    • (2003) Bull. Braz. Math. Soc. (N.S.) , vol.34 , pp. 231-249
    • Zuppa, C.1
  • 40
    • 0242271292 scopus 로고    scopus 로고
    • Good quality point sets and error estimates for moving least square approximations
    • Carlos Zuppa Good quality point sets and error estimates for moving least square approximations Appl. Numer. Math. 47 2003 575 585
    • (2003) Appl. Numer. Math. , vol.47 , pp. 575-585
    • Zuppa, C.1


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