Isogeometric Finite Element Analysis using B-spline Basis Functions: The Poisson Equation and the Biharmonic Equation

Abstract

In this thesis the finite element method with B-spline basis functions was implemented and tested for the Poisson equation and the Biharmonic equation in an isoparametric setting. The equations were solved on a unit square and a B-spline geometry in physical space for given boundary conditions. The convergence rate of the finite element method for p-degree spline basis functions was verified using a least squares approximation and Schoenberg's variation diminishing spline approximation for the lifting functions. For the Poisson equation weak enforcement by the classical Lagrange multiplier method was also considered.