Finite element methods for spherically symmetric elliptic equations:
This paper considers the numerical solution of elliptic partial differential equations in spherical domains. When all the functions involved are spherically symmetric (that is, they depend only on distance from the center of the domain), the problem can be replaced by an equivalent two-point boundar...
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| Hauptverfasser: | , , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
[New Haven, Conn.]
1977
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| Schriftenreihe: | Yale University <New Haven, Conn.> / Department of Computer Science: Research report
109 |
| Schlagworte: | |
| Zusammenfassung: | This paper considers the numerical solution of elliptic partial differential equations in spherical domains. When all the functions involved are spherically symmetric (that is, they depend only on distance from the center of the domain), the problem can be replaced by an equivalent two-point boundary value problem. The resulting problem is singular, but nevertheless has a smooth solution. It should therefore be possible to approximate the solution accurately using the Rayleigh-Ritz Galerkin method with a piecewise polynomial subspace on a quasiuniform mesh. Optimal-order error bounds will be obtained, showing that this procedure is theoretically well-founded. Instead of the usual Sobolev norms, norms are used which are appropriate to the original n-dimensional setting of the problem. |
Internformat
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| 100 | 1 | |a Eisenstat, Stanley S. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Finite element methods for spherically symmetric elliptic equations |c S. C. Eisenstat ; R. S. Schreiber ; M. H. Schultz |
| 264 | 1 | |a [New Haven, Conn.] |c 1977 | |
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| 490 | 1 | |a Yale University <New Haven, Conn.> / Department of Computer Science: Research report |v 109 | |
| 520 | 3 | |a This paper considers the numerical solution of elliptic partial differential equations in spherical domains. When all the functions involved are spherically symmetric (that is, they depend only on distance from the center of the domain), the problem can be replaced by an equivalent two-point boundary value problem. The resulting problem is singular, but nevertheless has a smooth solution. It should therefore be possible to approximate the solution accurately using the Rayleigh-Ritz Galerkin method with a piecewise polynomial subspace on a quasiuniform mesh. Optimal-order error bounds will be obtained, showing that this procedure is theoretically well-founded. Instead of the usual Sobolev norms, norms are used which are appropriate to the original n-dimensional setting of the problem. | |
| 650 | 4 | |a Galerkin method | |
| 650 | 4 | |a Rayleigh ritz method | |
| 650 | 7 | |a Approximation(mathematics) |2 dtict | |
| 650 | 7 | |a Boundary value problems |2 dtict | |
| 650 | 7 | |a Computations |2 dtict | |
| 650 | 7 | |a Ellipses |2 dtict | |
| 650 | 7 | |a Finite element analysis |2 dtict | |
| 650 | 7 | |a Partial differential equations |2 dtict | |
| 650 | 7 | |a Polynomials |2 dtict | |
| 650 | 7 | |a Splines(geometry) |2 dtict | |
| 650 | 7 | |a Theoretical Mathematics |2 scgdst | |
| 700 | 1 | |a Schreiber, Robert Samuel |e Verfasser |4 aut | |
| 700 | 1 | |a Schultz, Martin H. |e Verfasser |4 aut | |
| 810 | 2 | |a Department of Computer Science: Research report |t Yale University <New Haven, Conn.> |v 109 |w (DE-604)BV006663362 |9 109 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-006560407 | ||
Datensatz im Suchindex
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| author | Eisenstat, Stanley S. Schreiber, Robert Samuel Schultz, Martin H. |
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| id | DE-604.BV009905487 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:42:57Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006560407 |
| oclc_num | 227477539 |
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| owner_facet | DE-91G DE-BY-TUM |
| publishDate | 1977 |
| publishDateSearch | 1977 |
| publishDateSort | 1977 |
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| series2 | Yale University <New Haven, Conn.> / Department of Computer Science: Research report |
| spelling | Eisenstat, Stanley S. Verfasser aut Finite element methods for spherically symmetric elliptic equations S. C. Eisenstat ; R. S. Schreiber ; M. H. Schultz [New Haven, Conn.] 1977 txt rdacontent n rdamedia nc rdacarrier Yale University <New Haven, Conn.> / Department of Computer Science: Research report 109 This paper considers the numerical solution of elliptic partial differential equations in spherical domains. When all the functions involved are spherically symmetric (that is, they depend only on distance from the center of the domain), the problem can be replaced by an equivalent two-point boundary value problem. The resulting problem is singular, but nevertheless has a smooth solution. It should therefore be possible to approximate the solution accurately using the Rayleigh-Ritz Galerkin method with a piecewise polynomial subspace on a quasiuniform mesh. Optimal-order error bounds will be obtained, showing that this procedure is theoretically well-founded. Instead of the usual Sobolev norms, norms are used which are appropriate to the original n-dimensional setting of the problem. Galerkin method Rayleigh ritz method Approximation(mathematics) dtict Boundary value problems dtict Computations dtict Ellipses dtict Finite element analysis dtict Partial differential equations dtict Polynomials dtict Splines(geometry) dtict Theoretical Mathematics scgdst Schreiber, Robert Samuel Verfasser aut Schultz, Martin H. Verfasser aut Department of Computer Science: Research report Yale University <New Haven, Conn.> 109 (DE-604)BV006663362 109 |
| spellingShingle | Eisenstat, Stanley S. Schreiber, Robert Samuel Schultz, Martin H. Finite element methods for spherically symmetric elliptic equations Galerkin method Rayleigh ritz method Approximation(mathematics) dtict Boundary value problems dtict Computations dtict Ellipses dtict Finite element analysis dtict Partial differential equations dtict Polynomials dtict Splines(geometry) dtict Theoretical Mathematics scgdst |
| title | Finite element methods for spherically symmetric elliptic equations |
| title_auth | Finite element methods for spherically symmetric elliptic equations |
| title_exact_search | Finite element methods for spherically symmetric elliptic equations |
| title_full | Finite element methods for spherically symmetric elliptic equations S. C. Eisenstat ; R. S. Schreiber ; M. H. Schultz |
| title_fullStr | Finite element methods for spherically symmetric elliptic equations S. C. Eisenstat ; R. S. Schreiber ; M. H. Schultz |
| title_full_unstemmed | Finite element methods for spherically symmetric elliptic equations S. C. Eisenstat ; R. S. Schreiber ; M. H. Schultz |
| title_short | Finite element methods for spherically symmetric elliptic equations |
| title_sort | finite element methods for spherically symmetric elliptic equations |
| topic | Galerkin method Rayleigh ritz method Approximation(mathematics) dtict Boundary value problems dtict Computations dtict Ellipses dtict Finite element analysis dtict Partial differential equations dtict Polynomials dtict Splines(geometry) dtict Theoretical Mathematics scgdst |
| topic_facet | Galerkin method Rayleigh ritz method Approximation(mathematics) Boundary value problems Computations Ellipses Finite element analysis Partial differential equations Polynomials Splines(geometry) Theoretical Mathematics |
| volume_link | (DE-604)BV006663362 |
| work_keys_str_mv | AT eisenstatstanleys finiteelementmethodsforsphericallysymmetricellipticequations AT schreiberrobertsamuel finiteelementmethodsforsphericallysymmetricellipticequations AT schultzmartinh finiteelementmethodsforsphericallysymmetricellipticequations |