메뉴 건너뛰기




Volumn 72, Issue 243, 2003, Pages 1147-1177

Finite element superconvergence on Shishkin mesh for 2-D convection-diffusion problems

Author keywords

Boundary layer; Convection; Diffusion; Finite element method; Shishkin mesh; Singularly perturbed

Indexed keywords


EID: 0038468648     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-03-01486-8     Document Type: Article
Times cited : (114)

References (25)
  • 2
    • 0035612069 scopus 로고    scopus 로고
    • The hp-Version of the streamline diffusion finite element method in two space dimensions
    • MR 2001m:65168
    • K. Gerdes, J.M. Melenk, D. Schötzau and C. Schwab, The hp-Version of the Streamline Diffusion Finite Element Method in Two Space Dimensions, Math. Models Methods Appl. Sci. 11 (2001), 301-337. MR 2001m:65168
    • (2001) Math. Models Methods Appl. Sci. , vol.11 , pp. 301-337
    • Gerdes, K.1    Melenk, J.M.2    Schötzau, D.3    Schwab, C.4
  • 3
    • 0000787922 scopus 로고
    • Differentiability properties of solutions of the equation -εΔu+ru = f(x,y) in a square
    • MR 91e:35025
    • H. Han and R.B. Kellogg, Differentiability properties of solutions of the equation -εΔu+ru = f(x,y) in a square, SIAM J. Math. Anal. 21 (1990), 394-408. MR 91e:35025
    • (1990) SIAM J. Math. Anal. , vol.21 , pp. 394-408
    • Han, H.1    Kellogg, R.B.2
  • 4
    • 84966258545 scopus 로고
    • Crosswind smear and pointwise errors in the stream-line diffusion finite element method
    • MR 88i:65130
    • C. Johnson, A. Schatz, and L. Wahlbin, Crosswind smear and pointwise errors in the stream-line diffusion finite element method, Math. Comp. 49 (1987), 25-38. MR 88i:65130
    • (1987) Math. Comp. , vol.49 , pp. 25-38
    • Johnson, C.1    Schatz, A.2    Wahlbin, L.3
  • 5
    • 0000874375 scopus 로고
    • Boundary layers and corner singularities for a self-adjoint problem
    • M. Costabel, M. Dauge, and S. Nicaise eds., Marcel Dekker, New York, MR 95i:35046
    • R.B. Kellogg, Boundary layers and corner singularities for a self-adjoint problem, in Boundary Value Problems and Integral Equations in Non-smooth Domains, M. Costabel, M. Dauge, and S. Nicaise eds., Marcel Dekker, New York, 1995, 121-149. MR 95i:35046
    • (1995) Boundary Value Problems and Integral Equations in Non-smooth Domains , pp. 121-149
    • Kellogg, R.B.1
  • 6
    • 0003329886 scopus 로고    scopus 로고
    • Finite element methods: Superconvergence, post-processing, and a posteriori estimates
    • Marcel Dekker, Inc., New York, MR 98i:65003
    • M. Křížek, P. Neittaanmäki, and R. Stenberg (Eds.), Finite Element Methods: Superconvergence, Post-processing, and A Posteriori Estimates, Lecture Notes in Pure and Applied Mathematics, Vol. 196, Marcel Dekker, Inc., New York, 1998. MR 98i:65003
    • (1998) Lecture Notes in Pure and Applied Mathematics , vol.196
    • Křížek, M.1    Neittaanmäki, P.2    Stenberg, R.3
  • 7
    • 0031349640 scopus 로고    scopus 로고
    • Stream-line diffusion least-squares mixed finite element methods for convection-diffusion problems
    • MR 98k:76091
    • R.D. Lazarov, L. Tobiska, and P.S. Vassilevski, Stream-line diffusion least-squares mixed finite element methods for convection-diffusion problems, East-West J. Numer. Math. 5 (1997), 249-264. MR 98k:76091
    • (1997) East-West J. Numer. Math. , vol.5 , pp. 249-264
    • Lazarov, R.D.1    Tobiska, L.2    Vassilevski, P.S.3
  • 8
    • 0034436602 scopus 로고    scopus 로고
    • Uniformly convergent and superconvergence of mixed finite element methods for anisotropically refined grids
    • MR 2001f:65137
    • J. Li and M.F. Wheeler, Uniformly convergent and superconvergence of mixed finite element methods for anisotropically refined grids, SIAM J. Numer. Anal. 38 (2000), 770-798. MR 2001f:65137
    • (2000) SIAM J. Numer. Anal. , vol.38 , pp. 770-798
    • Li, J.1    Wheeler, M.F.2
  • 10
    • 0035885630 scopus 로고    scopus 로고
    • Asymptotic analysis and Shishkin-type decomposition for an elliptic convection-diffusion problem
    • MR 2002h:35039
    • T. Linß and M. Stynes, Asymptotic analysis and Shishkin-type decomposition for an elliptic convection-diffusion problem, J. Math. Anal. Appl. 261 (2001), 604-632. MR 2002h:35039
    • (2001) J. Math. Anal. Appl. , vol.261 , pp. 604-632
    • Linß, T.1    Stynes, M.2
  • 11
    • 0344307755 scopus 로고    scopus 로고
    • hp FEM for reaction-diffusion equations I: Robust exponential convergence
    • MR 99d:65333
    • J.M. Melenk and C. Schwab, hp FEM for reaction-diffusion equations I: Robust exponential convergence, SIAM J. Numer. Anal. 35 (1998), 1520-1557. MR 99d:65333
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 1520-1557
    • Melenk, J.M.1    Schwab, C.2
  • 12
    • 0032623107 scopus 로고    scopus 로고
    • Analytic regularity for a singularly perturbed problem
    • MR 2000b:35010
    • J.M. Melenk and C. Schwab, Analytic regularity for a singularly perturbed problem, SIAM J. Math. Anal. 30 (1999), 379-40. MR 2000b:35010
    • (1999) SIAM J. Math. Anal. , vol.30 , pp. 379-40
    • Melenk, J.M.1    Schwab, C.2
  • 15
    • 22044433064 scopus 로고    scopus 로고
    • Layer-adapted grids for singular perturbation problems
    • MR 99d:65301
    • H.-G. Roos, Layer-adapted grids for singular perturbation problems, ZAMM Z. Angew. Math. Mech. 78 (1998), 291-309. MR 99d:65301
    • (1998) ZAMM Z. Angew. Math. Mech. , vol.78 , pp. 291-309
    • Roos, H.-G.1
  • 17
    • 0001725828 scopus 로고    scopus 로고
    • Superconvergence in finite element methods and meshes that are locally symmetric with respect to a point
    • MR98f:65112
    • A.H. Schatz, T.H. Sloan, and L.B. Wahlbin, Superconvergence in finite element methods and meshes that are locally symmetric with respect to a point, SIAM J. Numer. Anal. 33 (1996), 505-521. MR98f:65112
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 505-521
    • Schatz, A.H.1    Sloan, T.H.2    Wahlbin, L.B.3
  • 18
    • 84966220357 scopus 로고
    • On the finite element method for singularly perturbed reaction-diffusion problems in two and one dimensions
    • MR 84c:65137
    • A.H. Schatz and L.B. Wahlbin, On the finite element method for singularly perturbed reaction-diffusion problems in two and one dimensions, Math. Comp. 40 (1983), 47-89. MR 84c:65137
    • (1983) Math. Comp. , vol.40 , pp. 47-89
    • Schatz, A.H.1    Wahlbin, L.B.2
  • 19
    • 0041622292 scopus 로고    scopus 로고
    • The p and hp versions of the finite element method for problems with boundary layers
    • MR 97a:65067
    • C. Schwab and M. Suri, The p and hp versions of the finite element method for problems with boundary layers, Math. Comp. 65 (1996), 1403-1429. MR 97a:65067
    • (1996) Math. Comp. , vol.65 , pp. 1403-1429
    • Schwab, C.1    Suri, M.2
  • 21
    • 0031240201 scopus 로고    scopus 로고
    • A uniformly convergent Galerkin method on a Shishkin mesh for a convection-diffusion problem
    • MR 99f:65177
    • M. Stynes and E. O'Riordan A uniformly convergent Galerkin method on a Shishkin mesh for a convection-diffusion problem, J. Math. Anal. Appl. 214 (1997), 36-54. MR 99f:65177
    • (1997) J. Math. Anal. Appl. , vol.214 , pp. 36-54
    • Stynes, M.1    O'Riordan, E.2
  • 22
    • 70350504045 scopus 로고
    • Local behavior in finite element methods
    • P.G. Ciarlet and J.L. Lions eds., North-Holland Publishing Company, Amsterdam, MR 92f:65001
    • L.B. Wahlbin, Local behavior in finite element methods, in Handbook of Numerical Analysis Vol. II, P.G. Ciarlet and J.L. Lions eds., North-Holland Publishing Company, Amsterdam, 1991, 353-522. MR 92f:65001
    • (1991) Handbook of Numerical Analysis , vol.2 , pp. 353-522
    • Wahlbin, L.B.1
  • 23
    • 0003271497 scopus 로고
    • Superconvergence in Galerkin finite element methods
    • Springer, Berlin, MR 98j:65083
    • L.B. Wahlbin, Superconvergence in Galerkin Finite Element Methods, Lecture Notes in Mathematics, Vol. 1605, Springer, Berlin, 1995. MR 98j:65083
    • (1995) Lecture Notes in Mathematics , vol.1605
    • Wahlbin, L.B.1
  • 24
    • 0036569433 scopus 로고    scopus 로고
    • Superconvergent approximation of singularly perturbed problems
    • Z. Zhang, Superconvergent approximation of singularly perturbed problems, Numer. Meth. PDEs 18 (2002), 374-395.
    • (2002) Numer. Meth. PDEs , vol.18 , pp. 374-395
    • Zhang, Z.1
  • 25
    • 0031542765 scopus 로고    scopus 로고
    • How accurate is the streamline diffusion finite element method?
    • MR97f:65171
    • G. Zhou, How accurate is the streamline diffusion finite element method? Math. Comp. 66 (1997), 31-44. MR97f:65171
    • (1997) Math. Comp. , vol.66 , pp. 31-44
    • Zhou, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.