A well-conditioned and optimally convergent XFEM for 3D linear elastic fracture

A variation of the extended finite element method for 3D fracture mechanics is
proposed. It utilizes global enrichment and point-wise as well as integral matching
of displacements of the standard and enriched elements in order to achieve higher
accuracy, optimal convergence rates and improved conditioning for two and three dimensional crack problems. A bespoke benchmark problem is introduced to determine
the method's accuracy in the general 3D case where it is demonstrated that
the proposed approach improves the accuracy and reduces the number of iterations
required for the iterative solution of the resulting system of equations by 40% for
moderately refined meshes and topological enrichment. Moreover, when a fixed enrichment
volume is used, the number of iterations required grows at a rate which is
reduced by a factor of 2 compared to standard XFEM, diminishing the number of
iterations by almost one order of magnitude.