메뉴 건너뛰기




Volumn 25, Issue 1, 2003, Pages 259-283

A posteriori error control in adaptive qualocation boundary element analysis for a logarithmic-kernel integral equation of the first kind

Author keywords

A posteriori error estimate; Adaptive algorithm; Boundary element method; Collocation method; Integral equations; Qualocation method

Indexed keywords

ADAPTIVE ALGORITHMS; APPROXIMATION THEORY; GALERKIN METHODS; INTEGRAL EQUATIONS; INTEGRATION;

EID: 1842511717     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827501399006     Document Type: Article
Times cited : (12)

References (39)
  • 2
    • 0000613724 scopus 로고
    • Error estimates for adaptive finite element computations
    • I. Babuška and W. C. Rheinboldt, Error estimates for adaptive finite element computations, SIAM J. Numer. Anal., 15 (1978), pp. 736-754.
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 736-754
    • Babuška, I.1    Rheinboldt, W.C.2
  • 3
    • 0023593007 scopus 로고
    • Asymptotically exact a posteriori error estimator for biquadratic elements
    • I. Babuška and D. Yu, Asymptotically exact a posteriori error estimator for biquadratic elements, Finite Elem. Anal. Des., 3 (1987), pp. 341-354.
    • (1987) Finite Elem. Anal. Des. , vol.3 , pp. 341-354
    • Babuška, I.1    Yu, D.2
  • 4
    • 0002853579 scopus 로고
    • Adaptive boundary element methods and adaptive finite element and boundary element coupling
    • M. Costabel, M. Dauge, and S. Nicaise, eds., Mercel Decker, New York
    • C. Carstensen, Adaptive boundary element methods and adaptive finite element and boundary element coupling, in Boundary Value Problems and Integral Equations on Non-smooth Domains, Lecture Notes in Pure and Appl. Math. 167, M. Costabel, M. Dauge, and S. Nicaise, eds., Mercel Decker, New York, 1995, pp. 47-58.
    • (1995) Boundary Value Problems and Integral Equations on Non-Smooth Domains, Lecture Notes in Pure and Appl. Math. , pp. 47-58
    • Carstensen, C.1
  • 5
    • 0030369991 scopus 로고    scopus 로고
    • Efficiency of a posteriori BEM error estimates for first kind integral equations on quasi-uniform meshes
    • C. Carstensen, Efficiency of a posteriori BEM error estimates for first kind integral equations on quasi-uniform meshes, Math. Comp., 65 (1996), pp. 69-84.
    • (1996) Math. Comp. , vol.65 , pp. 69-84
    • Carstensen, C.1
  • 6
    • 0031538766 scopus 로고    scopus 로고
    • An a posteriori error estimate for a first-kind integral equation
    • C. Carstensen, An a posteriori error estimate for a first-kind integral equation, Math. Comp., 66 (1997), pp. 69-84.
    • (1997) Math. Comp. , vol.66 , pp. 69-84
    • Carstensen, C.1
  • 7
  • 8
    • 0035399315 scopus 로고    scopus 로고
    • Mathematical foundation of a posteriori error estimates and adaptive mesh-refining algorithms for boundary integral equations of the first kind
    • C. Carstensen and B. Faermann, Mathematical foundation of a posteriori error estimates and adaptive mesh-refining algorithms for boundary integral equations of the first kind, Engineering Analysis with Boundary Elements, 25 (2001), pp. 497-509.
    • (2001) Engineering Analysis with Boundary Elements , vol.25 , pp. 497-509
    • Carstensen, C.1    Faermann, B.2
  • 9
    • 0000233779 scopus 로고    scopus 로고
    • A posteriori error estimates for hp-boundary element methods
    • C. Carstensen, S. A. Funken, and E. P. Stephan, A posteriori error estimates for hp-boundary element methods, Appl. Anal., 61 (1996), pp. 233-253.
    • (1996) Appl. Anal. , vol.61 , pp. 233-253
    • Carstensen, C.1    Funken, S.A.2    Stephan, E.P.3
  • 10
    • 0035545017 scopus 로고    scopus 로고
    • A posteriori error estimate and h-adaptive algorithm on surfaces for Symm's integral equation
    • C. Carstensen, M. Maischak, and E. P. Stephan, A posteriori error estimate and h-adaptive algorithm on surfaces for Symm's integral equation, Numer. Math., 90 (2001), pp. 197-213.
    • (2001) Numer. Math. , vol.90 , pp. 197-213
    • Carstensen, C.1    Maischak, M.2    Stephan, E.P.3
  • 11
    • 85160612011 scopus 로고    scopus 로고
    • Residual-based a posteriori error estimate for hypersingular equation on surfaces
    • to appear
    • C. Carstensen, M. Maischak, D. Praetorius, and E. P. Stephan, Residual-based a posteriori error estimate for hypersingular equation on surfaces, Numer. Math., to appear.
    • Numer. Math.
    • Carstensen, C.1    Maischak, M.2    Praetorius, D.3    Stephan, E.P.4
  • 12
    • 84968501793 scopus 로고
    • A posteriori error estimates for boundary element methods
    • C. Carstensen and E. P. Stephan, A posteriori error estimates for boundary element methods, Math. Comp., 64 (1995), pp. 483-500.
    • (1995) Math. Comp. , vol.64 , pp. 483-500
    • Carstensen, C.1    Stephan, E.P.2
  • 13
    • 0000621798 scopus 로고    scopus 로고
    • Adaptive boundary element methods for some first kind integral equations
    • C. Carstensen and E. P. Stephan, Adaptive boundary element methods for some first kind integral equations, SIAM J. Numer. Anal., 33 (1996), pp. 2166-2183.
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 2166-2183
    • Carstensen, C.1    Stephan, E.P.2
  • 14
    • 0000615142 scopus 로고
    • Spline qualocation methods for boundary integral equations
    • G. A. Chandler and I. H. Sloan, Spline qualocation methods for boundary integral equations, Numer. Math., 58 (1990), pp. 537-567.
    • (1990) Numer. Math. , vol.58 , pp. 537-567
    • Chandler, G.A.1    Sloan, I.H.2
  • 15
    • 0000438610 scopus 로고
    • Boundary integral operators on Lipschitz domains: Elementary results
    • M. Costabel, Boundary integral operators on Lipschitz domains: Elementary results, SIAM J. Math. Anal., 19 (1988), pp. 613-626.
    • (1988) SIAM J. Math. Anal. , vol.19 , pp. 613-626
    • Costabel, M.1
  • 16
    • 0032379842 scopus 로고    scopus 로고
    • Local a-posteriori error indicators for the Galerkin discretization of boundary integral equations
    • B. Faermann, Local a-posteriori error indicators for the Galerkin discretization of boundary integral equations, Numer. Math., 79 (1998), pp. 43-76.
    • (1998) Numer. Math. , vol.79 , pp. 43-76
    • Faermann, B.1
  • 17
    • 0034398971 scopus 로고    scopus 로고
    • Localization of the Aronszajn-Slobodeckij norm and application to adaptive boundary element methods. Part I. The two-dimensional case
    • B. Faermann, Localization of the Aronszajn-Slobodeckij norm and application to adaptive boundary element methods. Part I. The two-dimensional case, IMA J. Numer. Anal., 20 (2000), pp. 203-234.
    • (2000) IMA J. Numer. Anal. , vol.20 , pp. 203-234
    • Faermann, B.1
  • 18
    • 0036768415 scopus 로고    scopus 로고
    • Localization of the Aronszajn-Slobodeckij norm and application to adaptive boundary element methods. Part II. The three-dimensional case
    • B. Faermann, Localization of the Aronszajn-Slobodeckij norm and application to adaptive boundary element methods. Part II. The three-dimensional case, Numer. Math., 92 (2002), pp. 467-499.
    • (2002) Numer. Math. , vol.92 , pp. 467-499
    • Faermann, B.1
  • 19
    • 85160587334 scopus 로고    scopus 로고
    • Lokalisierungstechniken für Sobolev-Normen und Anwendung auf adaptive Randelementmethoden
    • Habilitation thesis, University of Kiel, Kiel, Germany
    • B. Faermann, Lokalisierungstechniken für Sobolev-Normen und Anwendung auf adaptive Randelementmethoden, Habilitation thesis, University of Kiel, Kiel, Germany, 2002.
    • (2002)
    • Faermann, B.1
  • 20
    • 0001557093 scopus 로고    scopus 로고
    • Asymptotic and a posteriori error estimates for boundary element solutions of hypersingular integral equations
    • M. Feistauer, G. C. Hsiao, and R. E. Kleinman, Asymptotic and a posteriori error estimates for boundary element solutions of hypersingular integral equations, SIAM J. Numer. Anal., 33 (1996), pp. 666-685.
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 666-685
    • Feistauer, M.1    Hsiao, G.C.2    Kleinman, R.E.3
  • 25
    • 0032688898 scopus 로고    scopus 로고
    • Analysis of hypersingular residual error estimates in boundary element methods for potential problems
    • G. Melon, G. H. Paulino, and S. Mukherjee, Analysis of hypersingular residual error estimates in boundary element methods for potential problems, Comput. Methods Appl. Mech. Engrg., 1868 (1999), pp. 449-473.
    • (1999) Comput. Methods Appl. Mech. Engrg. , vol.1868 , pp. 449-473
    • Melon, G.1    Paulino, G.H.2    Mukherjee, S.3
  • 27
    • 0003890212 scopus 로고
    • Méthodes directes en théorie des équations elliptiques
    • Academia, Prague
    • J. Nečas, Méthodes directes en théorie des équations elliptiques, Academia, Prague, 1967.
    • (1967)
    • Nečas, J.1
  • 29
    • 0001944121 scopus 로고
    • Adaptivity and accuracy estimation for FEM and BEM
    • I. Babuška, O. C. Zienkiewicz, J. Gago, and E. R. Oliveira, eds., Wiley, New York
    • E. Rank, Adaptivity and accuracy estimation for FEM and BEM, in Accuracy Estimates and Adaptive Refinements in FE Computations, I. Babuška, O. C. Zienkiewicz, J. Gago, and E. R. Oliveira, eds., Wiley, New York, 1986.
    • (1986) Accuracy Estimates and Adaptive Refinements in FE Computations
    • Rank, E.1
  • 31
    • 0002890708 scopus 로고    scopus 로고
    • A new a posteriori error estimator in adaptive direct boundary element methods
    • H. Schulz and O. Steinbach, A new a posteriori error estimator in adaptive direct boundary element methods. The Dirichlet problem, Calcolo, 37 (2000), pp. 79-96.
    • (2000) The Dirichlet Problem, Calcolo , vol.37 , pp. 79-96
    • Schulz, H.1    Steinbach, O.2
  • 33
    • 0033482032 scopus 로고    scopus 로고
    • On the extraction technique in boundary integral equations
    • Ch. Schwab and W. L. Wendland, On the extraction technique in boundary integral equations, Math. Comp., 68 (1999), pp. 91-122.
    • (1999) Math. Comp. , vol.68 , pp. 91-122
    • Schwab, Ch.1    Wendland, W.L.2
  • 34
    • 0035073897 scopus 로고    scopus 로고
    • Adaptive boundary element methods based on computational schemes for Sobolev norms
    • O. Steinbach, Adaptive boundary element methods based on computational schemes for Sobolev norms, SIAM J. Sci. Comput., 22 (2000), pp. 604-616.
    • (2000) SIAM J. Sci. Comput. , vol.22 , pp. 604-616
    • Steinbach, O.1
  • 35
    • 0001576476 scopus 로고
    • Adaptive BEM for strongly elliptic integral equations
    • W. L. Wendland and D. Yu, Adaptive BEM for strongly elliptic integral equations, Numer. Math., 53 (1988), pp. 539-558.
    • (1988) Numer. Math. , vol.53 , pp. 539-558
    • Wendland, W.L.1    Yu, D.2
  • 36
    • 0001200610 scopus 로고
    • A posteriori local error estimates of boundary element methods with some pseudo-differential equations on closed curves
    • W. L. Wendland and D. Yu, A posteriori local error estimates of boundary element methods with some pseudo-differential equations on closed curves, J. Comput. Math., 10 (1992), pp. 273-289.
    • (1992) J. Comput. Math. , vol.10 , pp. 273-289
    • Wendland, W.L.1    Yu, D.2
  • 37
    • 0001245997 scopus 로고
    • A-posteriori error estimates and adaptive approaches for some boundary element methods
    • C. A. Brebbia, W. L. Wendland, and G. Kuhn, eds., Springer-Verlag, Berlin
    • D. Yu, A-posteriori error estimates and adaptive approaches for some boundary element methods, in Boundary Elements 9, C. A. Brebbia, W. L. Wendland, and G. Kuhn, eds., Springer-Verlag, Berlin, 1987, pp. 241-256.
    • (1987) Boundary Elements , vol.9 , pp. 241-256
    • Yu, D.1
  • 38
    • 0000367886 scopus 로고
    • Self-adaptive boundary element methods
    • D. Yu, Self-adaptive boundary element methods, Z. Angew. Math. Mech., 68 (1988), pp. T435-T437.
    • (1988) Z. Angew. Math. Mech. , vol.68
    • Yu, D.1
  • 39
    • 0026241526 scopus 로고
    • Mathematical foundation of adaptive boundary element methods
    • D. Yu, Mathematical foundation of adaptive boundary element methods, Appl. Mech. Engrg., 91 (1991), pp. 1237-1243.
    • (1991) Appl. Mech. Engrg. , vol.91 , pp. 1237-1243
    • Yu, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.