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Volumn 36, Issue 2-3, 2001, Pages 129-154

Convergence and superconvergence analysis of finite element methods on highly nonuniform anisotropic meshes for singularly perturbed reaction-diffusion problems

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL GEOMETRY; CONVERGENCE OF NUMERICAL METHODS; FINITE ELEMENT METHOD; PERTURBATION TECHNIQUES; PROBLEM SOLVING; TENSORS;

EID: 0035254910     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(99)00145-2     Document Type: Article
Times cited : (38)

References (33)
  • 1
    • 0029289813 scopus 로고
    • High-order finite element methods for singularly perturbed elliptic and parabolic problems
    • Adjerid S., Aiffa M., Flaherty J.E. High-order finite element methods for singularly perturbed elliptic and parabolic problems. SIAM J. Appl. Math. 55:1995;520-543.
    • (1995) SIAM J. Appl. Math. , vol.55 , pp. 520-543
    • Adjerid, S.1    Aiffa, M.2    Flaherty, J.E.3
  • 2
    • 0000924189 scopus 로고    scopus 로고
    • Reliable and robust a posteriori error estimation for singularly perturbed reaction-diffusion problems
    • Ainsworth M., Babuška I. Reliable and robust a posteriori error estimation for singularly perturbed reaction-diffusion problems. SIAM J. Numer. Anal. 36:1999;331-353.
    • (1999) SIAM J. Numer. Anal. , vol.36 , pp. 331-353
    • Ainsworth, M.1    Babuška, I.2
  • 4
    • 0032045072 scopus 로고    scopus 로고
    • Anisotropic mesh refinement for a singularly perturbed reaction diffusion model problem
    • Apel T., Lube G. Anisotropic mesh refinement for a singularly perturbed reaction diffusion model problem. Appl. Numer. Math. 26:1998;415-433.
    • (1998) Appl. Numer. Math. , vol.26 , pp. 415-433
    • Apel, T.1    Lube, G.2
  • 7
    • 38249038947 scopus 로고
    • An adaptive characteristic Petrov-Galerkin finite element method for convection-dominated linear and nonlinear parabolic problems in one space variable
    • Demkowicz L., Oden J.T. An adaptive characteristic Petrov-Galerkin finite element method for convection-dominated linear and nonlinear parabolic problems in one space variable. J. Comput. Phys. 67:1986;188-213.
    • (1986) J. Comput. Phys. , vol.67 , pp. 188-213
    • Demkowicz, L.1    Oden, J.T.2
  • 8
    • 0000257740 scopus 로고    scopus 로고
    • Heterogeneous domain decomposition for singularly perturbed elliptic boundary value problems
    • Garbey M., Kaper H.G. Heterogeneous domain decomposition for singularly perturbed elliptic boundary value problems. SIAM J. Numer. Anal. 34:1997;1513-1544.
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 1513-1544
    • Garbey, M.1    Kaper, H.G.2
  • 12
    • 0007121464 scopus 로고    scopus 로고
    • Full-order convergence of a mixed finite element method for fourth-order elliptic equations
    • Li J. Full-order convergence of a mixed finite element method for fourth-order elliptic equations. J. Math. Anal. Appl. 230:1999;329-349.
    • (1999) J. Math. Anal. Appl. , vol.230 , pp. 329-349
    • Li, J.1
  • 13
    • 0031128557 scopus 로고    scopus 로고
    • Quasi-optimal uniformly convergent finite element methods for the elliptic boundary layer problem
    • Li J. Quasi-optimal uniformly convergent finite element methods for the elliptic boundary layer problem. Comput. Math. Appl. 33:1997;11-22.
    • (1997) Comput. Math. Appl. , vol.33 , pp. 11-22
    • Li, J.1
  • 14
    • 0031994221 scopus 로고    scopus 로고
    • Uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems I: Reaction-diffusion type
    • Li J., Navon I.M. Uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems I: reaction-diffusion type. Comput. Math. Appl. 35:1998;57-70.
    • (1998) Comput. Math. Appl. , vol.35 , pp. 57-70
    • Li, J.1    Navon, I.M.2
  • 15
    • 0032140876 scopus 로고    scopus 로고
    • Uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems II: Convection-diffusion type
    • Li J., Navon I.M. Uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems II: convection-diffusion type. Comput. Methods Appl. Mech. Engrg. 162:1998;49-78.
    • (1998) Comput. Methods Appl. Mech. Engrg. , vol.162 , pp. 49-78
    • Li, J.1    Navon, I.M.2
  • 16
    • 0032675494 scopus 로고    scopus 로고
    • Global uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems: Higher-order elements
    • Li J., Navon I.M. Global uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems: higher-order elements. Comput. Methods Appl. Mech. Engrg. 171:1999;1-23.
    • (1999) Comput. Methods Appl. Mech. Engrg. , vol.171 , pp. 1-23
    • Li, J.1    Navon, I.M.2
  • 18
    • 0041465934 scopus 로고
    • A rectangle test for Ciarlet-Raviart and Hermann-Miyoshi scheme
    • Hong Kong: Great Wall Culture Publ. Co.
    • Lin Q., Li J., Zhou A. A rectangle test for Ciarlet-Raviart and Hermann-Miyoshi scheme. Proc. Syst. Sci. and Syst. Engrg. 1991;230-233 Great Wall Culture Publ. Co. Hong Kong.
    • (1991) Proc. Syst. Sci. and Syst. Engrg. , pp. 230-233
    • Lin, Q.1    Li, J.2    Zhou, A.3
  • 25
    • 0027684524 scopus 로고
    • An anisotropic h-type mesh refinement strategy
    • Rachowicz W. An anisotropic h-type mesh refinement strategy. Comput. Methods Appl. Mech. Engrg. 109:1993;169-181.
    • (1993) Comput. Methods Appl. Mech. Engrg. , vol.109 , pp. 169-181
    • Rachowicz, W.1
  • 26
    • 22044433064 scopus 로고    scopus 로고
    • Layer-adapted grids for singular perturbation problems
    • Roos H.-G. Layer-adapted grids for singular perturbation problems. Z. Angew. Math. Mech. 78:1998;291-309.
    • (1998) Z. Angew. Math. Mech. , vol.78 , pp. 291-309
    • Roos, H.-G.1
  • 28
    • 84966220357 scopus 로고
    • On the finite element method for singularly perturbed reaction-diffusion problems in two and one dimensions
    • Schatz A.H., Wahlbin L.B. On the finite element method for singularly perturbed reaction-diffusion problems in two and one dimensions. Math. Comp. 40:1983;47-89.
    • (1983) Math. Comp. , vol.40 , pp. 47-89
    • Schatz, A.H.1    Wahlbin, L.B.2
  • 29
    • 0032507570 scopus 로고    scopus 로고
    • The hp finite element method for problems in mechanics with boundary layers
    • Schwab C., Suri M., Xenophontos C. The hp finite element method for problems in mechanics with boundary layers. Comput. Methods Appl. Mech. Engrg. 57:1998;311-334.
    • (1998) Comput. Methods Appl. Mech. Engrg. , vol.57 , pp. 311-334
    • Schwab, C.1    Suri, M.2    Xenophontos, C.3
  • 30
    • 0004189166 scopus 로고
    • Englewood Cliffs, NJ: Prentice-Hall
    • Schultz M.H. Spline Analysis. 1973;Prentice-Hall, Englewood Cliffs, NJ.
    • (1973) Spline Analysis
    • Schultz, M.H.1
  • 31
    • 0039758065 scopus 로고    scopus 로고
    • Robust a posteriori error estimators for a singularly perturbed reaction-diffusion equation
    • Verfürth R. Robust a posteriori error estimators for a singularly perturbed reaction-diffusion equation. Numer. Math. 78:1998;479-493.
    • (1998) Numer. Math. , vol.78 , pp. 479-493
    • Verfürth, R.1
  • 32
    • 0000667216 scopus 로고    scopus 로고
    • Uniform convergence of discretization error for a singular perturbation problem
    • Wesseling P. Uniform convergence of discretization error for a singular perturbation problem. Numer. Methods Partial Differential Equations. 12:1996;657-671.
    • (1996) Numer. Methods Partial Differential Equations , vol.12 , pp. 657-671
    • Wesseling, P.1
  • 33
    • 21844493210 scopus 로고
    • The full approximation accuracy for the Stream-Function-Vorticity-Pressure method
    • Zhou A., Li J. The full approximation accuracy for the Stream-Function-Vorticity-Pressure method. Numer. Math. 68:1994;427-435.
    • (1994) Numer. Math. , vol.68 , pp. 427-435
    • Zhou, A.1    Li, J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.