Isogeometric Analysis

Abstract

In this chapter we will present the method called isogeometric analysis based on the previous sections about finite element analysis and computer aided geometric design. Isogeometric analysis, just like FEM, is a method for solving partial differential equations and we use the same models introduced in Sec. 3.1 and the derived variational formulations shown in Sec. 3.2. Especially we can rely on the theoretical properties shown there and the Lax-Milgram theorem still ensures existence and uniqueness of the solution. Also Céea’s inequality holds and will be used for an error estimate. Instead of using the FEM function spaces we will rely on the spline spaces introduced for the geometric representation. This tackles the problem of mesh generation and exchanges the triangulations which are adapted to geometric data with the geometric representation itself. As basis functions B-splines or NURBS will be chosen due to their favorable properties.