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Title: Bivariate piecewise polynomials on curved domains, with applications to fully nonlinear PDE's
Author: Saeed, Abid
ISNI:       0000 0004 2746 3005
Awarding Body: University of Strathclyde
Current Institution: University of Strathclyde
Date of Award: 2012
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Using Bernstein-Bézier techniques we construct bivariate polynomial finite element spaces of arbitrary order for curved domains bounded by piecewise conics, which leads to an H¹ conforming isogeometric method to solve Dirichlet problems for second order elliptic partial differential equations. Numerical experiments for several test problems over curved domains show the robustness of the method. We then construct H² conforming polynomial finite element spaces for curved domains by extending the H¹ construction. These spaces are used in Böhmer's method for solving fully nonlinear elliptic equations. Numerical results for several benchmark problems including the Monge-Ampère equation over curved domains confirm the theoretical error bounds given by Böhmer.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available