IRTG Modern Inverse Problems (MIP)

Novel Stabilized Finite-Element Methods for Microstructured and Complex Fluids

08. Oktober 2018 | von

Prof. Marek Behr, Ph.D.

The project will advance the state of the art in the computational treatment of viscoelastic (VE) constitutive equations and similar model equations arising elsewhere. The applications of this research range from production engineering and melt-based forming processes (die swell of VE fluid shown in figure), to biomedical device design, to aerospace technology.

Low-order stabilized finite elements (FEM) are the workhorse of computational engineering, but are sensi- tive to element quality and stabilization parameters. Discontinuous Petrov-Galerkin (DPG) methods have a solid mathematical foundation and robustness, but are not yet used in industrial contexts. By merging the properties of FEM and DPG, robust method for microstructured fluids in industrial settings will be obtained.

The research goals of this project are:

  • Understanding of the stability and accuracy properties of two alternate finite element dis- cretization approaches;

  • Transfer of Discontinuous Petrov-Galerkin stability and accuracy advantages to low-order industrial FE formulations;

  • Insight into numerical behavior of sensitivities and adjoints required for design tasks in both approaches.

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