Isogeometric Collocation Method for Partial Differential Equations on Surfaces
This project aims to study the concept of collocation method for isogeometric analysis with NURBS. We first introduce the isogeometric concept and its main advantages compared to finite elements methods. We then present the isogeometric collocation method and compare it to the isogeometric Galerkin method in terms of computational cost and accuracy. Elliptic problems and parabolic problems (linear and non-linear) are considered. The convergence rates of the collocation method are numerically verified and the comparisons with the Galerkin method tend to show a better efficiency of the collocation method for even degrees of NURBS basis.