Geodesic
A Powell-Sabin finite element scheme for partial differential equations
Giorgio Giorgiani1 ; Hervé Guillard2 ; Boniface Nkonga2
1Maison de la Simulation USR 3441, Bâtiment 565 - Digiteo - PC 190, CEA Saclay, 91191 Gif-sur-Yvette cedex, France
2Inria Sophia-Antipolis 2004 Route des Lucioles, BP 93, 06902 Sophia-Antipolis Cedex and Univ. Nice Sophia Antipolis, LJAD, UMR 7351, 06100 Nice, France
ESAIM. Proceedings, Tome 53 (2016), pp. 64-76
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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.
DOI : 10.1051/proc/201653005

Giorgio Giorgiani  1   ; Hervé Guillard  2   ; Boniface Nkonga  2

1 Maison de la Simulation USR 3441, Bâtiment 565 - Digiteo - PC 190, CEA Saclay, 91191 Gif-sur-Yvette cedex, France
2 Inria Sophia-Antipolis 2004 Route des Lucioles, BP 93, 06902 Sophia-Antipolis Cedex and Univ. Nice Sophia Antipolis, LJAD, UMR 7351, 06100 Nice, France 
@article{EP_2016_53_a5,
     author = {Giorgio Giorgiani and Herv\'e Guillard and Boniface Nkonga},
     title = {A {Powell-Sabin} finite element scheme for partial differential equations},
     journal = {ESAIM. Proceedings},
     pages = {64--76},
     year = {2016},
     volume = {53},
     doi = {10.1051/proc/201653005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201653005/}
}
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Giorgio Giorgiani; Hervé Guillard; Boniface Nkonga. A Powell-Sabin finite element scheme for partial differential equations. ESAIM. Proceedings, Tome 53 (2016), pp. 64-76. doi: 10.1051/proc/201653005

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