This thesis investigates adaptive refinement strategies in isogeometric analysis (IGA) for the efficient and accurate numerical solution of problems with localized features, with particular emphasis on computational magnetostatics. Truncated hierarchical B-splines (THB-splines) enable local refinement, while multi-level Bézier extraction provides an element-wise representation compatible with standard finite element assembly. Adaptivity is driven by a least-squares a posteriori error estimator, which is extended to coupled rotor–stator problems using harmonic mortaring. The resulting framework is applied to 2-D magnetostatic simulations of permanent magnet synchronous machines (PMSMs). In addition, anisotropic refinement is investigated using decoupled patchwork B-splines (DPB-splines), allowing patch-wise and directionally selective refinement while remaining compatible with Bézier extraction.