DOI: 10.1016/s0045-7825(96)01087-0. The partition of unity finite element method: Basic theory and applications

The partition of unity finite element method: Basic theory and applications

10.1016/s0045-7825(96)01087-0

Crossref journal-article

Elsevier BV

Computer Methods in Applied Mechanics and Engineering (78)

Bibliography

Melenk, J. M., & BabuÅ¡ka, I. (1996). The partition of unity finite element method: Basic theory and applications. Computer Methods in Applied Mechanics and Engineering, 139(1â4), 289â314.

Authors 2

J.M. Melenk (first)
I. Babuška (additional)

References 20 Referenced 2,655

{'key': '10.1016/S0045-7825(96)01087-0_BIB1', 'series-title': 'Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations', 'year': '1972'} / Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (1972)
I. Babuška and J.E. Osborn, Private communication.
{'key': '10.1016/S0045-7825(96)01087-0_BIB3', 'series-title': 'Integral Operators in the Theory of Linear Partial Differential Equations', 'author': 'Bergman', 'year': '1961'} / Integral Operators in the Theory of Linear Partial Differential Equations by Bergman (1961)
10.1137/0914029 / SIAM J. Sci. Comput. / A transpose-free quasi-minimal residual algorithm for non-hermitian linear systems by Freund (1993)
{'key': '10.1016/S0045-7825(96)01087-0_BIB5', 'series-title': 'Table of Integrals, Series and Products', 'author': 'Gradshtein', 'year': '1980'} / Table of Integrals, Series and Products by Gradshtein (1980)
{'key': '10.1016/S0045-7825(96)01087-0_BIB6', 'series-title': 'Boundary Methods: An Algebraic Theory', 'author': 'Herrera', 'year': '1984'} / Boundary Methods: An Algebraic Theory by Herrera (1984)
{'key': '10.1016/S0045-7825(96)01087-0_BIB7', 'series-title': 'Linear Integral Equations', 'author': 'Kress', 'year': '1989'} / Linear Integral Equations by Kress (1989)
{'key': '10.1016/S0045-7825(96)01087-0_BIB8', 'article-title': 'On generalized finite element methods', 'author': 'Melenk', 'year': '1995'} / On generalized finite element methods by Melenk (1995)
{'key': '10.1016/S0045-7825(96)01087-0_BIB9', 'first-page': '294', 'volume': 'Vol. 3 of 1', 'author': 'Mergelyan', 'year': '1962'} by Mergelyan (1962)
{'key': '10.1016/S0045-7825(96)01087-0_BIB10', 'series-title': 'Some Basic Problems of the Mathematical Theory of Elasticity', 'author': 'Muskhelishvili', 'year': '1963'} / Some Basic Problems of the Mathematical Theory of Elasticity by Muskhelishvili (1963)
10.1016/0045-7825(92)90164-F / Comput. Methods Appl. Mech. Engrg. / The p-version of the finite element method for the elliptic boundary value problems with interfaces by Oh (1992)
10.1016/S0021-9991(95)90017-9 / J. Comput. Phys. / The method of auxiliary mapping for the finite element solutions of elasticity problems containing singularities by Oh (1995)
10.1137/0731051 / SIAM J. Numer. Anal. / Special finite element methods for a class of second order elliptic problems with rough coefficients by Babuška (1994)
10.1016/0045-7825(95)00890-X / Comput. Methods Appl. Mech. Engrg. / A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution by Babuška (1995)
I. Babuška and J.M. Melenk, The partition of unity method, Int. J. Numer. Methods Engrg., in press.
I. Babuška and Z. Zhang, The partition of unity finite element method for the elastically supported beam, to appear.
10.1007/BF01279030 / Mathematische Zeitschrift / Über Polynome, die zu einer gegebenen Kurve der komplexen Ebene gehören by Szegö (1921)
10.1002/nme.1620380303 / Int. J. Numer. Methods Engrg. / A Galerkin least squares finite element method for the two-dimensional Helmholtz equation by Thomson (1995)
{'key': '10.1016/S0045-7825(96)01087-0_BIB19', 'series-title': 'New Methods for Solving Elliptic Equations', 'author': 'Vekua', 'year': '1967'} / New Methods for Solving Elliptic Equations by Vekua (1967)
{'key': '10.1016/S0045-7825(96)01087-0_BIB20', 'article-title': 'Interpolation and Approximation by Rational Functions in the Complex Domain', 'volume': 'Vol. 20', 'author': 'Walsh', 'year': '1960'} / Interpolation and Approximation by Rational Functions in the Complex Domain by Walsh (1960)

Dates

Type	When
Created	23 years ago (July 25, 2002, 9:05 a.m.)
Deposited	6 years, 3 months ago (April 25, 2019, 12:55 a.m.)
Indexed	33 minutes ago (Aug. 21, 2025, 6:57 a.m.)
Issued	28 years, 8 months ago (Dec. 1, 1996)
Published	28 years, 8 months ago (Dec. 1, 1996)
Published Print	28 years, 8 months ago (Dec. 1, 1996)

Funders 0

None

BibTeX

@article{Melenk_1996, title={The partition of unity finite element method: Basic theory and applications}, volume={139}, ISSN={0045-7825}, url={http://dx.doi.org/10.1016/s0045-7825(96)01087-0}, DOI={10.1016/s0045-7825(96)01087-0}, number={1–4}, journal={Computer Methods in Applied Mechanics and Engineering}, publisher={Elsevier BV}, author={Melenk, J.M. and Babuška, I.}, year={1996}, month=dec, pages={289–314} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        21
      ]
    ],
    "date-time": "2025-08-21T10:57:19Z",
    "timestamp": 1755773839644
  },
  "reference-count": 20,
  "publisher": "Elsevier BV",
  "issue": "1-4",
  "license": [
    {
      "start": {
        "date-parts": [
          [
            1996,
            12,
            1
          ]
        ],
        "date-time": "1996-12-01T00:00:00Z",
        "timestamp": 849398400000
      },
      "content-version": "tdm",
      "delay-in-days": 0,
      "URL": "https://www.elsevier.com/tdm/userlicense/1.0/"
    }
  ],
  "content-domain": {
    "domain": [],
    "crossmark-restriction": false
  },
  "published-print": {
    "date-parts": [
      [
        1996,
        12
      ]
    ]
  },
  "DOI": "10.1016/s0045-7825(96)01087-0",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2002,
        7,
        25
      ]
    ],
    "date-time": "2002-07-25T13:05:15Z",
    "timestamp": 1027602315000
  },
  "page": "289-314",
  "source": "Crossref",
  "is-referenced-by-count": 2655,
  "title": "The partition of unity finite element method: Basic theory and applications",
  "prefix": "10.1016",
  "volume": "139",
  "author": [
    {
      "given": "J.M.",
      "family": "Melenk",
      "sequence": "first",
      "affiliation": []
    },
    {
      "given": "I.",
      "family": "Babu\u0161ka",
      "sequence": "additional",
      "affiliation": []
    }
  ],
  "member": "78",
  "reference": [
    {
      "key": "10.1016/S0045-7825(96)01087-0_BIB1",
      "series-title": "Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations",
      "year": "1972"
    },
    {
      "key": "10.1016/S0045-7825(96)01087-0_BIB2",
      "unstructured": "I. Babu\u0161ka and J.E. Osborn, Private communication."
    },
    {
      "key": "10.1016/S0045-7825(96)01087-0_BIB3",
      "series-title": "Integral Operators in the Theory of Linear Partial Differential Equations",
      "author": "Bergman",
      "year": "1961"
    },
    {
      "issue": "2",
      "key": "10.1016/S0045-7825(96)01087-0_BIB4",
      "doi-asserted-by": "crossref",
      "first-page": "470",
      "DOI": "10.1137/0914029",
      "article-title": "A transpose-free quasi-minimal residual algorithm for non-hermitian linear systems",
      "volume": "14",
      "author": "Freund",
      "year": "1993",
      "journal-title": "SIAM J. Sci. Comput."
    },
    {
      "key": "10.1016/S0045-7825(96)01087-0_BIB5",
      "series-title": "Table of Integrals, Series and Products",
      "author": "Gradshtein",
      "year": "1980"
    },
    {
      "key": "10.1016/S0045-7825(96)01087-0_BIB6",
      "series-title": "Boundary Methods: An Algebraic Theory",
      "author": "Herrera",
      "year": "1984"
    },
    {
      "key": "10.1016/S0045-7825(96)01087-0_BIB7",
      "series-title": "Linear Integral Equations",
      "author": "Kress",
      "year": "1989"
    },
    {
      "key": "10.1016/S0045-7825(96)01087-0_BIB8",
      "article-title": "On generalized finite element methods",
      "author": "Melenk",
      "year": "1995"
    },
    {
      "key": "10.1016/S0045-7825(96)01087-0_BIB9",
      "first-page": "294",
      "volume": "Vol. 3 of 1",
      "author": "Mergelyan",
      "year": "1962"
    },
    {
      "key": "10.1016/S0045-7825(96)01087-0_BIB10",
      "series-title": "Some Basic Problems of the Mathematical Theory of Elasticity",
      "author": "Muskhelishvili",
      "year": "1963"
    },
    {
      "key": "10.1016/S0045-7825(96)01087-0_BIB11",
      "doi-asserted-by": "crossref",
      "first-page": "211",
      "DOI": "10.1016/0045-7825(92)90164-F",
      "article-title": "The p-version of the finite element method for the elliptic boundary value problems with interfaces",
      "volume": "97",
      "author": "Oh",
      "year": "1992",
      "journal-title": "Comput. Methods Appl. Mech. Engrg."
    },
    {
      "issue": "2",
      "key": "10.1016/S0045-7825(96)01087-0_BIB12",
      "doi-asserted-by": "crossref",
      "first-page": "193",
      "DOI": "10.1016/S0021-9991(95)90017-9",
      "article-title": "The method of auxiliary mapping for the finite element solutions of elasticity problems containing singularities",
      "volume": "121",
      "author": "Oh",
      "year": "1995",
      "journal-title": "J. Comput. Phys."
    },
    {
      "key": "10.1016/S0045-7825(96)01087-0_BIB13",
      "doi-asserted-by": "crossref",
      "first-page": "945",
      "DOI": "10.1137/0731051",
      "article-title": "Special finite element methods for a class of second order elliptic problems with rough coefficients",
      "volume": "31",
      "author": "Babu\u0161ka",
      "year": "1994",
      "journal-title": "SIAM J. Numer. Anal."
    },
    {
      "key": "10.1016/S0045-7825(96)01087-0_BIB14",
      "doi-asserted-by": "crossref",
      "first-page": "325",
      "DOI": "10.1016/0045-7825(95)00890-X",
      "article-title": "A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution",
      "volume": "128",
      "author": "Babu\u0161ka",
      "year": "1995",
      "journal-title": "Comput. Methods Appl. Mech. Engrg."
    },
    {
      "key": "10.1016/S0045-7825(96)01087-0_BIB15",
      "unstructured": "I. Babu\u0161ka and J.M. Melenk, The partition of unity method, Int. J. Numer. Methods Engrg., in press."
    },
    {
      "key": "10.1016/S0045-7825(96)01087-0_BIB16",
      "unstructured": "I. Babu\u0161ka and Z. Zhang, The partition of unity finite element method for the elastically supported beam, to appear."
    },
    {
      "key": "10.1016/S0045-7825(96)01087-0_BIB17",
      "doi-asserted-by": "crossref",
      "first-page": "218",
      "DOI": "10.1007/BF01279030",
      "article-title": "\u00dcber Polynome, die zu einer gegebenen Kurve der komplexen Ebene geh\u00f6ren",
      "volume": "9",
      "author": "Szeg\u00f6",
      "year": "1921",
      "journal-title": "Mathematische Zeitschrift"
    },
    {
      "key": "10.1016/S0045-7825(96)01087-0_BIB18",
      "doi-asserted-by": "crossref",
      "first-page": "371",
      "DOI": "10.1002/nme.1620380303",
      "article-title": "A Galerkin least squares finite element method for the two-dimensional Helmholtz equation",
      "volume": "38",
      "author": "Thomson",
      "year": "1995",
      "journal-title": "Int. J. Numer. Methods Engrg."
    },
    {
      "key": "10.1016/S0045-7825(96)01087-0_BIB19",
      "series-title": "New Methods for Solving Elliptic Equations",
      "author": "Vekua",
      "year": "1967"
    },
    {
      "key": "10.1016/S0045-7825(96)01087-0_BIB20",
      "article-title": "Interpolation and Approximation by Rational Functions in the Complex Domain",
      "volume": "Vol. 20",
      "author": "Walsh",
      "year": "1960"
    }
  ],
  "container-title": "Computer Methods in Applied Mechanics and Engineering",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://api.elsevier.com/content/article/PII:S0045782596010870?httpAccept=text/xml",
      "content-type": "text/xml",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "https://api.elsevier.com/content/article/PII:S0045782596010870?httpAccept=text/plain",
      "content-type": "text/plain",
      "content-version": "vor",
      "intended-application": "text-mining"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2019,
        4,
        25
      ]
    ],
    "date-time": "2019-04-25T04:55:30Z",
    "timestamp": 1556168130000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://linkinghub.elsevier.com/retrieve/pii/S0045782596010870"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1996,
        12
      ]
    ]
  },
  "references-count": 20,
  "journal-issue": {
    "issue": "1-4",
    "published-print": {
      "date-parts": [
        [
          1996,
          12
        ]
      ]
    }
  },
  "alternative-id": [
    "S0045782596010870"
  ],
  "URL": "http://dx.doi.org/10.1016/S0045-7825(96)01087-0",
  "relation": {},
  "ISSN": [
    "0045-7825"
  ],
  "subject": [],
  "container-title-short": "Computer Methods in Applied Mechanics and Engineering",
  "published": {
    "date-parts": [
      [
        1996,
        12
      ]
    ]
  }
}