Weak imposition of Dirichlet boundary conditions for analyses using Powell–Sabin B‐splines

Powell–Sabin B-splines are enjoying an increased use in the analysis of solids and fluids, including fracture propagation. However, B-spline interpolation does not hold Kronecker delta property and, therefore, imposition Dirichlet boundary conditions is as straightforward for standard finite elements. Herein, we discuss applicability various approaches developed to date weak analyses which employ B-splines. We take elasticity propagation using phase-field modeling a benchmark problem. first succinctly recapitulate model brittle fracture, encapsulates linear elasticity, its discretization As baseline solution impose strong sense, this Lagrange multiplier, penalty, Nitsche's methods, well methods based on Hellinger-Reissner principle, linked multiplier method modified version.