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Volumn 4, Issue 3-4, 1997, Pages 607-632

Approximation with harmonic and generalized harmonic polynomials in the partition of unity method

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; DIFFERENTIAL EQUATIONS; POLYNOMIALS;

EID: 0031357421     PISSN: 1232308X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (65)

References (47)
  • 1
    • 0000967937 scopus 로고
    • The boundary layer for the Reissner-Mindlin plate model
    • D. N. Arnold, R. S. Falk. The boundary layer for the Reissner-Mindlin plate model. SIAM J. Math. Anal, 21: 281-312, 1990.
    • (1990) SIAM J. Math. Anal , vol.21 , pp. 281-312
    • Arnold, D.N.1    Falk, R.S.2
  • 2
  • 6
    • 0007259480 scopus 로고
    • Application of the method of the kernel function for solving boundary value problems
    • S. Bergman, J. Herriot. Application of the method of the kernel function for solving boundary value problems. Numer. Math., 3: 209-225, 1961.
    • (1961) Numer. Math. , vol.3 , pp. 209-225
    • Bergman, S.1    Herriot, J.2
  • 7
    • 3943062663 scopus 로고
    • Numerical solution of boundary-value problems by the method of integral operators
    • S. Bergman, J. Herriot. Numerical solution of boundary-value problems by the method of integral operators. Numer. Math., 7: 42-65, 1965.
    • (1965) Numer. Math. , vol.7 , pp. 42-65
    • Bergman, S.1    Herriot, J.2
  • 9
    • 0016072753 scopus 로고
    • On the rate of convergence of the Bergman-Vekua method for the numerical solution of elliptic boundary value problems
    • Stanley C. Eisenstat. On the rate of convergence of the Bergman-Vekua method for the numerical solution of elliptic boundary value problems. SIAM J. Numer. Anal., 11: 654-680, 1974.
    • (1974) SIAM J. Numer. Anal. , vol.11 , pp. 654-680
    • Eisenstat, S.C.1
  • 10
    • 0000568642 scopus 로고
    • On the use of singular functions with the finite element method
    • G. Fix, S. Gulati, G. I. Wakoff. On the use of singular functions with the finite element method. J. Comput. Phys., 13: 209-228, 1973.
    • (1973) J. Comput. Phys. , vol.13 , pp. 209-228
    • Fix, G.1    Gulati, S.2    Wakoff, G.I.3
  • 11
    • 0001031880 scopus 로고
    • A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems
    • R. W. Freund. A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems. SIAM J. Sci. Comput, 14(2): 470-482, 1993.
    • (1993) SIAM J. Sci. Comput , vol.14 , Issue.2 , pp. 470-482
    • Freund, R.W.1
  • 13
    • 3943104190 scopus 로고
    • A survey of I.N. Vekua's theory of elliptic partial differential equations with analytic coefficients
    • P. Henrici. A survey of I.N. Vekua's theory of elliptic partial differential equations with analytic coefficients. Z. Angew. Math. Phys., 1957.
    • (1957) Z. Angew. Math. Phys.
    • Henrici, P.1
  • 15
    • 0022696572 scopus 로고
    • The hybrid-Trefftz finite element model and its application to plate bending
    • J. Jirousek, Lan Guex. The hybrid-Trefftz finite element model and its application to plate bending. Internat. J. Numer. Meths. Engrg., 23: 651-693, 1986.
    • (1986) Internat. J. Numer. Meths. Engrg. , vol.23 , pp. 651-693
    • Jirousek, J.1    Guex, L.2
  • 16
    • 84987041447 scopus 로고
    • Hybrid-TrefTtz plane elasticity elements with p-method capabilities
    • J. Jirousek, A. Venkatesh. Hybrid-TrefTtz plane elasticity elements with p-method capabilities. Internat. J. Numer. Meths. Engrg., 35: 1443-1472, 1992.
    • (1992) Internat. J. Numer. Meths. Engrg. , vol.35 , pp. 1443-1472
    • Jirousek, J.1    Venkatesh, A.2
  • 17
    • 0025229330 scopus 로고
    • Multiquadrics-a scattered data approximation scheme with applications to computational fluid-dynamics-I surface approximations and partial derivative estimates
    • E.J. Kansa. Multiquadrics-a scattered data approximation scheme with applications to computational fluid-dynamics-I surface approximations and partial derivative estimates. Computers and Mathematics with Applications, 19(8/9): 127-145, 1990.
    • (1990) Computers and Mathematics with Applications , vol.19 , Issue.8-9 , pp. 127-145
    • Kansa, E.J.1
  • 18
    • 0025210711 scopus 로고
    • Multiquadrics-a scattered data approximation scheme with applications to computational fluid-dynamics-II solutions to parabolic, hyperbolic, and elliptic partial differential equations
    • E.J. Kansa. Multiquadrics-a scattered data approximation scheme with applications to computational fluid-dynamics-II solutions to parabolic, hyperbolic, and elliptic partial differential equations. Computers and Mathematics with Applications, 19(8/9): 147-161, 1990.
    • (1990) Computers and Mathematics with Applications , vol.19 , Issue.8-9 , pp. 147-161
    • Kansa, E.J.1
  • 25
    • 0030380578 scopus 로고    scopus 로고
    • The partition of unity finite element method: Basic theory and applications
    • J.M. Melenk, I. Babuska. The partition of unity finite element method: Basic theory and applications. Comput. Meths. Appl. Mech. Engrg., 39: 289-314, 1996.
    • (1996) Comput. Meths. Appl. Mech. Engrg. , vol.39 , pp. 289-314
    • Melenk, J.M.1    Babuska, I.2
  • 28
    • 0027035536 scopus 로고
    • Generalizing the finite element method: Diffuse approximation and diffuse elements
    • B. Nayroles, G. Touzot, P. Villon. Generalizing the finite element method: diffuse approximation and diffuse elements. Computational Mechanics, 10: 307-318, 1992.
    • (1992) Computational Mechanics , vol.10 , pp. 307-318
    • Nayroles, B.1    Touzot, G.2    Villon, P.3
  • 29
    • 0026872323 scopus 로고
    • The p-version of the finite element method for the elliptic boundary value problems with interfaces
    • Hae-Soo Oh, I. Babuška. The p-version of the finite element method for the elliptic boundary value problems with interfaces. Comput. Meths. Appl. Mech. Engrg., 97: 211-231, 1992.
    • (1992) Comput. Meths. Appl. Mech. Engrg. , vol.97 , pp. 211-231
    • Oh, H.-S.1    Babuška, I.2
  • 30
    • 0001685521 scopus 로고
    • The method of auxiliary mapping for the finite element solutions of elasticity problems containing singularities
    • Hae-Soo Oh, I. Babuška. The method of auxiliary mapping for the finite element solutions of elasticity problems containing singularities. J. Comput. Phys. 121(2): 193-212, 1995.
    • (1995) J. Comput. Phys. , vol.121 , Issue.2 , pp. 193-212
    • Oh, H.-S.1    Babuška, I.2
  • 32
    • 0002596552 scopus 로고
    • Creating surfaces from scattered data using radial basis functions
    • M. Daehlen, T. Lyche, L.L. Schumaker, eds.
    • R. Schaback. Creating surfaces from scattered data using radial basis functions. In: M. Daehlen, T. Lyche, L.L. Schumaker, eds., Mathematical Methods in CAGD III, pages 1-21, 1995.
    • (1995) Mathematical Methods in CAGD III , pp. 1-21
    • Schaback, R.1
  • 33
    • 0015482532 scopus 로고
    • Constructive approximation of solutions to linear elliptic boundary value problems
    • N. L. Schryer. Constructive approximation of solutions to linear elliptic boundary value problems. SIAM J. Numer. Anal, 9: 546-572, 1972.
    • (1972) SIAM J. Numer. Anal , vol.9 , pp. 546-572
    • Schryer, N.L.1
  • 34
    • 38249033049 scopus 로고
    • Information-based numerical practice
    • I. Babuška. Information-based numerical practice. Journal of Complexity, 3: 331-346, 1987.
    • (1987) Journal of Complexity , vol.3 , pp. 331-346
    • Babuška, I.1
  • 35
    • 0028483749 scopus 로고
    • Special finite element methods for a class of second order elliptic problems with rough coefficients
    • I. Babuška, G. Caloz, J. Osborn. Special finite element methods for a class of second order elliptic problems with rough coefficients. SIAM J. Numer. Anal., 31: 945-981, 1994.
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 945-981
    • Babuška, I.1    Caloz, G.2    Osborn, J.3
  • 36
    • 0007102981 scopus 로고
    • On the regularity of elasticity problems with piecewise analytic data
    • I. Babuška, B. Guo. On the regularity of elasticity problems with piecewise analytic data. Advances in Applied Mathematics, 14: 307-347, 1993.
    • (1993) Advances in Applied Mathematics , vol.14 , pp. 307-347
    • Babuška, I.1    Guo, B.2
  • 37
    • 0029487468 scopus 로고
    • A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution
    • I. Babuška, F. Ihlenburg, E. Paik, S. Sauter. A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution. Comput. Meths. Appl. Mech. Engrg., 128: 325-360, 1995.
    • (1995) Comput. Meths. Appl. Mech. Engrg. , vol.128 , pp. 325-360
    • Babuška, I.1    Ihlenburg, F.2    Paik, E.3    Sauter, S.4
  • 39
    • 3943053809 scopus 로고    scopus 로고
    • The partition of unity finite element method for the elastically supported beam
    • I. Babuška, Z. Zhang. The partition of unity finite element method for the elastically supported beam, (to appear in Comput. Meths. Appl. Mech. Engrg.)
    • Comput. Meths. Appl. Mech. Engrg.
    • Babuška, I.1    Zhang, Z.2
  • 40
    • 0038990445 scopus 로고
    • Die Kombination des modifizierten Trefftzschen Verfahrens mit der Methode der finiten Elemente
    • K.E. Buck, D.W. Scharpf, E. Stein, W. Ernst, editors
    • E. Stein. Die Kombination des modifizierten Trefftzschen Verfahrens mit der Methode der finiten Elemente. In K.E. Buck, D.W. Scharpf, E. Stein, W. Ernst, editors, Finite Elemente in der Statik. 1973.
    • (1973) Finite Elemente in der Statik
    • Stein, E.1
  • 41
    • 0038735900 scopus 로고
    • Über Polynome, die zu einer gegebenen Kurve der komplexen Ebene gehören
    • G. Szegö. Über Polynome, die zu einer gegebenen Kurve der komplexen Ebene gehören. Mathematische Zeitschrift, 9: 218-270, 1921.
    • (1921) Mathematische Zeitschrift , vol.9 , pp. 218-270
    • Szegö, G.1
  • 42
    • 0029239896 scopus 로고
    • A Galerkin least squares finite element method for the two-dimensional Helmholtz equation
    • L.L. Thomson, P.M. Pinsky. A Galerkin least squares finite element method for the two-dimensional Helmholtz equation. Internat. J. Numer. Meths. Engrg., 38: 371-397, 1995.
    • (1995) Internat. J. Numer. Meths. Engrg. , vol.38 , pp. 371-397
    • Thomson, L.L.1    Pinsky, P.M.2
  • 45
    • 0029512082 scopus 로고
    • On trial functions applied in the generalized Trefftz method
    • A.P. Zielinski. On trial functions applied in the generalized Trefftz method. Advances in Engineering Software, 24, 1995.
    • (1995) Advances in Engineering Software , vol.24
    • Zielinski, A.P.1
  • 46
    • 0022026528 scopus 로고
    • Generalized finite element analysis with T-complete boundary solution functions
    • O.G. Zienkiewicz, A.P. Zielinski. Generalized finite element analysis with T-complete boundary solution functions. Internat. J. Numer. Meths. Engrg., 21: 509-528, 1985.
    • (1985) Internat. J. Numer. Meths. Engrg. , vol.21 , pp. 509-528
    • Zienkiewicz, O.G.1    Zielinski, A.P.2
  • 47
    • 0002387960 scopus 로고
    • On n-widths in Sobolev spaces and applications to elliptic boundary value problems
    • J. W. Jerome. On n-widths in Sobolev spaces and applications to elliptic boundary value problems. J. Math. Anal. Appl., 20: 201-215, 1970.
    • (1970) J. Math. Anal. Appl. , vol.20 , pp. 201-215
    • Jerome, J.W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.