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

• Applicants: Dr. Mirjam Walloth; Professor Dr. Thomas Wick; Professor Dr. Winnifried Wollner
• Subject Area: Mechanics ; Mathematics
• Term: from 2017 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 392587580

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.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1748: Reliable Simulation Techniques in Solid Mechanics - Development of Non-Standard Discretisation Methods, Mechanical and Mathematical Analysis