CutIGA with Basis Function Removal
For researchers in isogeometric analysis, this provides a stabilization technique for cut finite element methods with theoretical guarantees.
The paper develops a cut isogeometric method for second-order elliptic problems, removing basis functions with small domain intersection to stabilize the method, and proves that the convergence order in the energy norm is unaffected by the removal, with improved bounds due to B-spline regularity.
We consider a cut isogeometric method, where the boundary of the domain is allowed to cut through the background mesh in an arbitrary fashion for a second order elliptic model problem. In order to stabilize the method on the cut boundary we remove basis functions which have small intersection with the computational domain. We determine criteria on the intersection which guarantee that the order of convergence in the energy norm is not affected by the removal. The higher order regularity of the B-spline basis functions leads to improved bounds compared to standard Lagrange elements.