A Powell-Sabin finite element scheme for partial differential equations

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...

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Main Authors: Giorgiani Giorgio, Guillard Hervé, Nkonga Boniface
Format: Article
Language:English
Published: EDP Sciences 2016-03-01
Series:ESAIM: Proceedings and Surveys
Online Access:http://dx.doi.org/10.1051/proc/201653005
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spelling doaj-59b37f186fe9436caba7e11f50de71862021-07-15T14:11:56ZengEDP 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
collection DOAJ
language English
format Article
sources DOAJ
author Giorgiani Giorgio
Guillard Hervé
Nkonga Boniface
spellingShingle Giorgiani Giorgio
Guillard Hervé
Nkonga Boniface
A Powell-Sabin finite element scheme for partial differential equations
ESAIM: Proceedings and Surveys
author_facet Giorgiani Giorgio
Guillard Hervé
Nkonga Boniface
author_sort Giorgiani Giorgio
title A Powell-Sabin finite element scheme for partial differential equations
title_short 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_sort powell-sabin finite element scheme for partial differential equations
publisher EDP Sciences
series ESAIM: Proceedings and Surveys
issn 2267-3059
publishDate 2016-03-01
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.
url http://dx.doi.org/10.1051/proc/201653005
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AT guillardherve apowellsabinfiniteelementschemeforpartialdifferentialequations
AT nkongaboniface apowellsabinfiniteelementschemeforpartialdifferentialequations
AT giorgianigiorgio powellsabinfiniteelementschemeforpartialdifferentialequations
AT guillardherve powellsabinfiniteelementschemeforpartialdifferentialequations
AT nkongaboniface powellsabinfiniteelementschemeforpartialdifferentialequations
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