Structure Preserving Adaptive Enriched Galerkin Methods for Pressure-Driven 3D Fracture Phase-Field Models

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The project is concerned with the development of innovative enriched Galerkin methods for the reliable simulation of pressure-driven fracture problems.Within this scope the project will consider the sound modeling of pressure driven fractures in (quasi-)incompressible materials for quasi-static and dynamic fracture-propagation. Emphasis will be given to the analysis of the incompressible limit by combining mixed formulations together with recent pressure robust discretizations for the Stokes-equation.This will be complemented by designing convergent adaptive mesh-refinement schemes based on new efficient error estimators for the variational inequality associated with the fracture irreversibility.