메뉴 건너뛰기




Volumn 37, Issue 1-2, 2001, Pages 241-255

Sufficient conditions for uniform convergence on layer-adapted grids

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; PERTURBATION TECHNIQUES; PROBLEM SOLVING;

EID: 0343897889     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(00)00043-X     Document Type: Article
Times cited : (44)

References (28)
  • 1
    • 0000475515 scopus 로고    scopus 로고
    • A study of difference schemes with the first derivative approximated by a central difference ratio
    • Andreev V.B., Kopteva N.V. A study of difference schemes with the first derivative approximated by a central difference ratio. Comput. Math. Math. Phys. 36:1996;1065-1078.
    • (1996) Comput. Math. Math. Phys. , vol.36 , pp. 1065-1078
    • Andreev, V.B.1    Kopteva, N.V.2
  • 2
    • 0042611999 scopus 로고    scopus 로고
    • On the convergence, uniform with respect to a small parameter, of monotone three-point difference approximations
    • Andreev V.B., Kopteva N.V. On the convergence, uniform with respect to a small parameter, of monotone three-point difference approximations. Differ. Equations. 34:1998;921-929.
    • (1998) Differ. Equations , vol.34 , pp. 921-929
    • Andreev, V.B.1    Kopteva, N.V.2
  • 3
    • 0006582614 scopus 로고
    • The uniform convergence with respect to a small parameter of A.A. Samarski's monotone scheme and its modification
    • Andreev V.B., Savin I.A. The uniform convergence with respect to a small parameter of A.A. Samarski's monotone scheme and its modification. Comput. Math. Math. Phys. 35:1995;739-752.
    • (1995) Comput. Math. Math. Phys. , vol.35 , pp. 739-752
    • Andreev, V.B.1    Savin, I.A.2
  • 4
    • 0001238824 scopus 로고
    • On the optimization of methods for solving boundary value problems with boundary layers
    • (in Russian)
    • Bakhvalov A.S. On the optimization of methods for solving boundary value problems with boundary layers. Zh. Vychisl. Mat. i Mat. Fiz. 9:1969;841-859. (in Russian).
    • (1969) Zh. Vychisl. Mat. I Mat. Fiz. , vol.9 , pp. 841-859
    • Bakhvalov, A.S.1
  • 5
    • 0034300742 scopus 로고    scopus 로고
    • Convergence analysis of finite difference approximations on equidistributed grids to a singularly perturbed boundary value problem
    • Beckett G.M., Mackenzie J.A. Convergence analysis of finite difference approximations on equidistributed grids to a singularly perturbed boundary value problem. Appl. Numer. Math. 35:2000;87-109.
    • (2000) Appl. Numer. Math. , vol.35 , pp. 87-109
    • Beckett, G.M.1    MacKenzie, J.A.2
  • 6
    • 0042968779 scopus 로고
    • The numerical solution of a nonlinear boundary value problem with a small parameter effecting the highest derivative
    • (in Russian)
    • Boglaev I.P. The numerical solution of a nonlinear boundary value problem with a small parameter effecting the highest derivative. Zh. Vychisl. Mat. i Mat. Fiz. 24:1984;1649-1656. (in Russian).
    • (1984) Zh. Vychisl. Mat. I Mat. Fiz. , vol.24 , pp. 1649-1656
    • Boglaev, I.P.1
  • 8
    • 85031534035 scopus 로고    scopus 로고
    • Application of the over-set grid technique to a model singular perturbation problem
    • to appear
    • E.D. Havik, P.W. Hemker, W. Hoffmann, Application of the over-set grid technique to a model singular perturbation problem, Computing, to appear.
    • Computing
    • Havik, E.D.1    Hemker, P.W.2    Hoffmann, W.3
  • 9
    • 84966216257 scopus 로고
    • Analysis of some difference approximations for a singular perturbation problem without turning points
    • Kellogg R.B., Tsan A. Analysis of some difference approximations for a singular perturbation problem without turning points. Math. Comp. 32:1978;1025-1039.
    • (1978) Math. Comp. , vol.32 , pp. 1025-1039
    • Kellogg, R.B.1    Tsan, A.2
  • 10
    • 0042756247 scopus 로고    scopus 로고
    • On the uniform with respect to a small parameter convergence of the central difference scheme on condensing meshes
    • Kopteva N.V. On the uniform with respect to a small parameter convergence of the central difference scheme on condensing meshes. Comput. Math. Math. Phys. 39:1999;1669-1685.
    • (1999) Comput. Math. Math. Phys. , vol.39 , pp. 1669-1685
    • Kopteva, N.V.1
  • 12
    • 0344614030 scopus 로고    scopus 로고
    • An upwind difference scheme on a novel Shishkin-type mesh for a linear convection-diffusion problem
    • Linß T. An upwind difference scheme on a novel Shishkin-type mesh for a linear convection-diffusion problem. J. Comput. Appl. Math. 110:1999;93-104.
    • (1999) J. Comput. Appl. Math. , vol.110 , pp. 93-104
    • Linß, T.1
  • 14
    • 85031525157 scopus 로고    scopus 로고
    • Uniform pointwise convergence of finite difference schemes using grid equidistribution
    • to appear
    • T. Linß, Uniform pointwise convergence of finite difference schemes using grid equidistribution, Computing, to appear.
    • Computing
    • Linß, T.1
  • 15
    • 85031532183 scopus 로고    scopus 로고
    • Analysis of a Galerkin finite element method on a Bakhvalov-Shishkin mesh for a linear convection-diffusion problem
    • to appear
    • T. Linß, Analysis of a Galerkin finite element method on a Bakhvalov-Shishkin mesh for a linear convection-diffusion problem, IMA J. Numer. Anal., to appear.
    • IMA J. Numer. Anal.
    • Linß, T.1
  • 16
    • 85031526370 scopus 로고    scopus 로고
    • Uniform pointwise convergence on Shishkin-type meshes for quasilinear convection-diffusion problems
    • to appear
    • T. Linß, H.-G. Roos, R. Vulanović, Uniform pointwise convergence on Shishkin-type meshes for quasilinear convection-diffusion problems, SIAM J. Numer. Anal., to appear.
    • SIAM J. Numer. Anal.
    • Linß, T.1    Roos, H.-G.2    Vulanović, R.3
  • 17
    • 0033112611 scopus 로고    scopus 로고
    • Uniform convergence analysis of a convection-diffusion boundary value problem on an adaptive grid
    • Mackenzie J.A. Uniform convergence analysis of a convection-diffusion boundary value problem on an adaptive grid. IMA J. Numer. Anal. 19:1999;233-249.
    • (1999) IMA J. Numer. Anal. , vol.19 , pp. 233-249
    • MacKenzie, J.A.1
  • 19
    • 0003329938 scopus 로고
    • Singular Perturbation Methods for Ordinary Differential Equations
    • New York: Springer
    • O'Malley R.E. Jr. Singular Perturbation Methods for Ordinary Differential Equations. Applied Mathematical Sciences. 89:1991;Springer, New York.
    • (1991) Applied Mathematical Sciences , vol.89
    • O'Malley R.E. Jr1
  • 20
    • 0032689583 scopus 로고    scopus 로고
    • Analysis of difference approximations to a singularly perturbed two-point boundary value problem on an adaptively generated grid
    • Qiu Y., Sloan D.M. Analysis of difference approximations to a singularly perturbed two-point boundary value problem on an adaptively generated grid. J. Comput. Appl. Math. 101:1999;1-25.
    • (1999) J. Comput. Appl. Math. , vol.101 , pp. 1-25
    • Qiu, Y.1    Sloan, D.M.2
  • 21
    • 0344718020 scopus 로고    scopus 로고
    • Sufficient conditions for uniform convergence on layer adapted grids
    • Roos H.-G., Linß T. Sufficient conditions for uniform convergence on layer adapted grids. Computing. 63:1999;27-45.
    • (1999) Computing , vol.63 , pp. 27-45
    • Roos, H.-G.1    Linß, T.2
  • 22
    • 0000310890 scopus 로고    scopus 로고
    • A comparison of the finite element method on Shishkin and Gartland-type meshes for convection-diffusion problems
    • Roos H.-G., Skalický T. A comparison of the finite element method on Shishkin and Gartland-type meshes for convection-diffusion problems. CWI Quarterly. 10:1997;277-300.
    • (1997) CWI Quarterly , vol.10 , pp. 277-300
    • Roos, H.-G.1    Skalický, T.2
  • 26
    • 22444455088 scopus 로고    scopus 로고
    • A finite difference analysis of a streamline diffusion method on a Shishkin mesh
    • Stynes M., Tobiska L. A finite difference analysis of a streamline diffusion method on a Shishkin mesh. Numer. Algorithms. 18:1998;337-360.
    • (1998) Numer. Algorithms , vol.18 , pp. 337-360
    • Stynes, M.1    Tobiska, L.2
  • 27
    • 0002560723 scopus 로고
    • A uniform numerical method for quasilinear singular perturbation problems without turning points
    • Vulanović R. A uniform numerical method for quasilinear singular perturbation problems without turning points. Computing. 41:1989;97-106.
    • (1989) Computing , vol.41 , pp. 97-106
    • Vulanović, R.1
  • 28
    • 85031521948 scopus 로고    scopus 로고
    • A priori meshes for singularly perturbed quasilinear two-point boundary value problems
    • to appear
    • R. Vulanović, A priori meshes for singularly perturbed quasilinear two-point boundary value problems, IMA J. Numer. Anal., to appear.
    • IMA J. Numer. Anal.
    • Vulanović, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.