An accurate strategy for computing reaction forces and fluxes on trimmed locally refined meshes

Abstract The finite element method is classically based on nodal Lagrange basis functions defined conforming meshes. In this context, total reaction forces are commonly computed from the so-called “nodal forces”, yielding higher accuracy and convergence rates than reactions obtained differentiated primal solution (“direct” method). cell isogeometric analysis promise to improve interoperability of computer-aided design engineering, enabling a direct approach numerical simulation trimmed geometries. However, body-unfitted meshes preclude use classic algorithms. This work shows that can perform particularly poorly for immersed methods. Instead, conservative be equilibrium expressions given by weak problem formulation, superior typical reactions. also extended non-interpolatory functions, such as (truncated) hierarchical B-splines.