A Powell-Sabin finite element scheme for partial differential equations
In this paper are analyzed finite element methods based on Powell-Sabin splines, for the solution of partial differential equations in two dimensions. PS splines are piecewise quadratic polynomials defined on a triangulation of the domain, and exhibit a global C1 cont...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
EDP Sciences
2016-03-01
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| Series: | ESAIM: Proceedings and Surveys |
| Online Access: | http://dx.doi.org/10.1051/proc/201653005 |
| _version_ | 1797972038343720960 |
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| author | Giorgiani Giorgio Guillard Hervé Nkonga Boniface |
| author_facet | Giorgiani Giorgio Guillard Hervé Nkonga Boniface |
| author_sort | Giorgiani Giorgio |
| collection | DOAJ |
| description | In this paper are analyzed finite element methods based on Powell-Sabin splines, for the
solution of partial differential equations in two dimensions. PS splines are piecewise
quadratic polynomials defined on a triangulation of the domain, and exhibit a global
C1 continuity. Critical issues when
dealing with PS splines, and described in this work, are the construction of the shape
functions and the imposition of the boundary conditions. The PS finite element method is
used at first to solve an elliptic problem describing plasma equilibrium in a tokamak.
Finally, a transient convective problem is also considered, and a stabilized formulation
is presented. |
| first_indexed | 2024-04-11T03:41:00Z |
| format | Article |
| id | doaj.art-59b37f186fe9436caba7e11f50de7186 |
| institution | Directory Open Access Journal |
| issn | 2267-3059 |
| language | English |
| last_indexed | 2024-04-11T03:41:00Z |
| publishDate | 2016-03-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | ESAIM: Proceedings and Surveys |
| spelling | doaj.art-59b37f186fe9436caba7e11f50de71862023-01-02T03:40:01ZengEDP SciencesESAIM: Proceedings and Surveys2267-30592016-03-0153647610.1051/proc/201653005proc165305A Powell-Sabin finite element scheme for partial differential equationsGiorgiani Giorgio0Guillard Hervé1Nkonga Boniface2Maison de la Simulation USR 3441, Bâtiment 565 - Digiteo - PC 190, CEA SaclayInria Sophia-Antipolis 2004 Route des Lucioles, BP 93, 06902 Sophia-Antipolis Cedex and Univ. Nice Sophia Antipolis, LJAD, UMR 7351Inria Sophia-Antipolis 2004 Route des Lucioles, BP 93, 06902 Sophia-Antipolis Cedex and Univ. Nice Sophia Antipolis, LJAD, UMR 7351In this paper are analyzed finite element methods based on Powell-Sabin splines, for the solution of partial differential equations in two dimensions. PS splines are piecewise quadratic polynomials defined on a triangulation of the domain, and exhibit a global C1 continuity. Critical issues when dealing with PS splines, and described in this work, are the construction of the shape functions and the imposition of the boundary conditions. The PS finite element method is used at first to solve an elliptic problem describing plasma equilibrium in a tokamak. Finally, a transient convective problem is also considered, and a stabilized formulation is presented.http://dx.doi.org/10.1051/proc/201653005 |
| spellingShingle | Giorgiani Giorgio Guillard Hervé Nkonga Boniface A Powell-Sabin finite element scheme for partial differential equations ESAIM: Proceedings and Surveys |
| title | A Powell-Sabin finite element scheme for partial differential
equations |
| title_full | A Powell-Sabin finite element scheme for partial differential
equations |
| title_fullStr | A Powell-Sabin finite element scheme for partial differential
equations |
| title_full_unstemmed | A Powell-Sabin finite element scheme for partial differential
equations |
| title_short | A Powell-Sabin finite element scheme for partial differential
equations |
| title_sort | powell sabin finite element scheme for partial differential equations |
| url | http://dx.doi.org/10.1051/proc/201653005 |
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