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Stability of incompressible formulations enriched with X-FEM

X-FEM has emerged as a useful and practical approach to capture strong and weak discontinuities and is now implemented in commercial codes. However its use for incompressible materials was not studied until this seminal paper where the incompressibility issue is addressed, discussed, and solved. Stable numerical solutions of incompressible materials (fluid or solid) employing an X-FEM methodology are justified within the context of the proposed methodology. This paper identifies the interpolations that are used in X-FEM for incompressible materials. This is a collaborative work with Professor Moes who is the recognized leading authority in the field.