Comput Mech manuscript No. (will be inserted by the editor) Well-conditioning global-local analysis using stable generalized/extended finite element method for linear elastic fracture mechanics Mohammad Malekan · Felicio Bruzzi Barros Received: date / Accepted: date Abstract Using the locally-enriched strategy to enrich a small/local part of the problem by generalized/extended finite element method (G/XFEM) leads to non-optimal convergence rate and ill-conditioning system of equa- tions due to presence of blending elements. The local enrichment can be chosen from polynomial, singular, branch or numerical types. The so-called stable version of G/XFEM method provides a well-conditioning ap- proach when only singular functions are used in the blending elements. This paper combines numeric en- richment functions obtained from global-local G/XFEM method with the polynomial enrichment along with a well-conditioning approach, stable G/XFEM, in order to show the robustness and effectiveness of the approach. In global-local G/XFEM, the enrichment functions are constructed numerically from the solution of a local problem. Furthermore, several enrichment strategies are adopted along with the global-local enrichment. The re- sults obtained with these enrichments strategies are dis- cussed in detail, considering convergence rate in strain energy, growth rate of condition number, and computa- tional processing. Numerical experiments show that us- ing geometrical enrichment along with stable G/XFEM for global-local strategy improves the convergence rate and the conditioning of the problem. In addition, re- Mohammad Malekan Graduate Program in Structural Engineering (PROPEEs), School of Engineering, Federal University of Minas Gerais (UFMG), Belo Horizonte, MG, Brazil E-mail: mmalekan1986@gmail.com Felicio Bruzzi Barros Graduate Program in Structural Engineering (PROPEEs), School of Engineering, Federal University of Minas Gerais (UFMG), Belo Horizonte, MG, Brazil Tel.: +55-31-34091995 Fax: +55-31-32381973 E-mail: felicio@dees.ufmg.br sults shows that using polynomial enrichment for global problem simultaneously with global-local enrichments lead to ill-conditioned system matrices and bad conver- gence rate. Keywords Partition of Unity · Stable General- ized/eXtended FEM · Condition Number · Global- Local · Blending Element 1 Introduction Computational tools have been increasingly improved during the last two decades. Among them Finite El- ement Method (FEM) has been widely used for the numerical modeling of structural problems [23, 11, 49]. However, this method has its own limitations with frac- ture mechanics problems. Generalized or eXtended Fi- nite Element Method (G/XFEM) [29, 40, 15, 8, 31], have become popular numerical tools for the simulation of discontinuous phenomena for fracture problems. This method models the crack by enriching (locally or glob- ally) functions of Partition of Unity (PU) type, such as the standard FEM approximation functions with singu- lar/discontinuous enrichment functions or with numer- ical functions that represent well the physical behav- ior of the crack tip. Enrichment functions multiply the original FEM functions and smooth/non-smooth solu- tions can be modeled independently of the mesh. This functions can be analytically known or numerically gen- erated, as observed by Strouboulis et al [41]. Although the G/XFEM offers advantages over the classical FEM approximation, there are still critical is- sues that bring some difficulties in practical aspects. Two issues addressed in [44]: the extra nodal degrees of freedom (DOFs) and linear dependence between stan- dard FEM and enrichment functions. The extra DOF