메뉴 건너뛰기




Volumn 36, Issue 6, 1999, Pages 1878-1900

Uniform a priori estimates for singularly perturbed elliptic equations in multidimensions

Author keywords

A priori estimates; Boundary layer; Error estimates; Singularly perturbed elliptic equation

Indexed keywords


EID: 0010574196     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142998341325     Document Type: Article
Times cited : (23)

References (25)
  • 1
    • 0008803371 scopus 로고
    • Defect correction methods for convection dominated convection-diffusion problems
    • O. AXELSSON AND W. LAYTON, Defect correction methods for convection dominated convection-diffusion problems, RAIRO Modél. Math. Anal. Numér., 24 (1990), pp. 423-455.
    • (1990) RAIRO Modél. Math. Anal. Numér. , vol.24 , pp. 423-455
    • Axelsson, O.1    Layton, W.2
  • 3
    • 0015727120 scopus 로고
    • Perturbations singulières et prolongements maximaux d'opérateurs positifs
    • C. BARDOS, D. BRÉZIS, AND H. BRÉZIS, Perturbations singulières et prolongements maximaux d'opérateurs positifs, Arch. Rational Mech. Anal., 53 (1973), pp. 69-100.
    • (1973) Arch. Rational Mech. Anal. , vol.53 , pp. 69-100
    • Bardos, C.1    Brézis, D.2    Brézis, H.3
  • 4
    • 84967782989 scopus 로고
    • Maximal positive boundary value problems as limits of singular perturbation problems
    • C. BARDOS AND J. RAUCH, Maximal positive boundary value problems as limits of singular perturbation problems, Trans. Amer. Math. Soc., 270 (1982), pp. 377-408.
    • (1982) Trans. Amer. Math. Soc. , vol.270 , pp. 377-408
    • Bardos, C.1    Rauch, J.2
  • 6
    • 0040357964 scopus 로고
    • The asymptotic behavior of the first real eigenvalue of second order elliptic operators with a small parameter in the highest derivatives, II
    • A. DEVINATZ, R. ELLIS, AND A. FRIEDMAN, The asymptotic behavior of the first real eigenvalue of second order elliptic operators with a small parameter in the highest derivatives, II, Indiana Univ. Math. J., 23 (1974), pp. 991-1011.
    • (1974) Indiana Univ. Math. J. , vol.23 , pp. 991-1011
    • Devinatz, A.1    Ellis, R.2    Friedman, A.3
  • 7
    • 0004585543 scopus 로고    scopus 로고
    • A priori estimates for the solution of convection-diffusion problems and interpolation on shishkin meshes
    • M. DOBROWOLSKI AND H.-G. ROOS, A priori estimates for the solution of convection-diffusion problems and interpolation on shishkin meshes, Z. Anal. Anwendungen, 16 (1997), pp. 1001-1012.
    • (1997) Z. Anal. Anwendungen , vol.16 , pp. 1001-1012
    • Dobrowolski, M.1    Roos, H.-G.2
  • 8
    • 0000493883 scopus 로고    scopus 로고
    • Uniform error estimates for an exponentially fitted finite element method for singularly perturbed elliptic equations
    • W. DÖRFLER, Uniform error estimates for an exponentially fitted finite element method for singularly perturbed elliptic equations, SIAM J. Numer. Anal., 36 (1999), pp. 1709-1738.
    • (1999) SIAM J. Numer. Anal. , vol.36 , pp. 1709-1738
    • Dörfler, W.1
  • 14
    • 84966258545 scopus 로고
    • Crosswind smear and pointwise errors in streamline diffusion finite element methods
    • C. JOHNSON, A. H. SCHATZ, AND L. B. WAHLBIN, Crosswind smear and pointwise errors in streamline diffusion finite element methods, Math. Comp., 49 (1987), pp. 25-38.
    • (1987) Math. Comp. , vol.49 , pp. 25-38
    • Johnson, C.1    Schatz, A.H.2    Wahlbin, L.B.3
  • 15
    • 0000874375 scopus 로고
    • Boundary layers and corner singularities for a self-adjoint problem
    • Boundary Value Problems and Integral Equations in Nonsmooth Domains, Proceedings of the conference held at the CIRM, Luminy, France, 1993, Marcel Dekker, New York
    • R. B. KELLOGG, Boundary layers and corner singularities for a self-adjoint problem, in Boundary Value Problems and Integral Equations in Nonsmooth Domains, Proceedings of the conference held at the CIRM, Luminy, France, 1993, Lecture Notes in Pure and Appl. Math. 167, Marcel Dekker, New York, 1995, pp. 121-149.
    • (1995) Lecture Notes in Pure and Appl. Math. , vol.167 , pp. 121-149
    • Kellogg, R.B.1
  • 20
    • 84968465448 scopus 로고
    • Pointwise a posteriori error estimates for elliptic problems on highly graded meshes
    • R. H. NOCHETTO, Pointwise a posteriori error estimates for elliptic problems on highly graded meshes, Math. Comp., 64 (1995), pp. 1-22.
    • (1995) Math. Comp. , vol.64 , pp. 1-22
    • Nochetto, R.H.1
  • 21
    • 84966240353 scopus 로고
    • A globally uniformly convergent finite element method for a singularly perturbed elliptic problem in two dimensions
    • E. O'RIORDAN AND M. STYNES, A globally uniformly convergent finite element method for a singularly perturbed elliptic problem in two dimensions, Math. Comp., 57 (1991), pp. 47-62.
    • (1991) Math. Comp. , vol.57 , pp. 47-62
    • O'Riordan, E.1    Stynes, M.2
  • 22
    • 0030213109 scopus 로고    scopus 로고
    • A novel nonconforming uniformly convergent finite element method in two dimensions
    • H.-G. ROOS, D. ADAM, AND A. FELGENHAUER, A novel nonconforming uniformly convergent finite element method in two dimensions, J. Math. Anal. Appl., 201 (1996), pp. 715-755.
    • (1996) J. Math. Anal. Appl. , vol.201 , pp. 715-755
    • Roos, H.-G.1    Adam, D.2    Felgenhauer, A.3
  • 25
    • 0003274014 scopus 로고
    • Non-equidistant finite difference methods for elliptic singular perturbation methods
    • J. J. H. Miller, ed., Boole Press, Dublin
    • R. VULANOVIĆ, Non-equidistant finite difference methods for elliptic singular perturbation methods, in Computational Methods for Boundary and Interior Layers in Several Dimensions, J. J. H. Miller, ed., Boole Press, Dublin, 1991, pp. 203-223.
    • (1991) Computational Methods for Boundary and Interior Layers in Several Dimensions , pp. 203-223
    • Vulanović, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.