Fig. 42

Convergence rates on the relative errors with respect to mesh refinement for the circular inclusion problem. The enrichment strategies are: linear shape functions and linear enrichment function (weak, linear, linear), quadratic shape functions and linear enrichment (weak, quadratic, linear) and quadratic shape functions and quadratic enrichment function (weak, quadratic, quadratic). Two models based on the enrichment designed for strong discontinuities, using Lagrange multipliers to enforce the continuity of the displacement through the interface have also been investigated: one with quadratic shape functions and a linear approximation of the level set (strong, quadratic, linear) and one with quadratic shape functions and a quadratic approximation of the level set (strong, quadratic, quadratic)