Volume 53, March 2016CEMRACS 2014 – Numerical Modeling of Plasmas
|Page(s)||64 - 76|
|Published online||01 April 2016|
A Powell-Sabin finite element scheme for partial differential equations
1 Maison de la Simulation USR 3441,
Bâtiment 565 - Digiteo - PC 190, CEA Saclay, 91191
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
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.
© EDP Sciences, SMAI 2016
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