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Logo: Graduate School MUSIC
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Logo: Graduate School MUSIC
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Mathematical Analysis

The role of applied mathematics in this interdisciplinary graduate school is to provide the basic methodologies for the analytical and numerical treatment of the processes coupled via interfaces arising in various applications. Within this area of research, treatment of the interface problems will be based on mixed finite element methods or the coupling of finite elements and boundary elements in conjunction with multiscale methods for spatial and temporal scales which are described in the application problems defined in the engineering projects. The advantage of mixed approaches is that process variables directly involved in the interface coupling, like in the domain decomposition approach for scale bridging, are approximated by suitable finite element spaces. This leads to simpler coupling formulations in combination with more accurate approximations. Both h- and p-refinements are investigated. A toolbox of suitable procedures for the treatment of interface coupling is created together with the scientists from the other groups in MUSIC.

Projects with internal funding:

 PhD projects currently available

 Projects with external funding/topics for Ph.D. theses:

  • Treatment of interface problems using mixed finite element methods
  • Coupling of finite elements and boundary elements for multiscale analysis
  • Adaptive methods with h- and p-refinements for multilevel analysis
  • Error-controlled finite element analysis in a multiscale environment
  • Multilevel solvers for multilevel problems
  • Robust solvers for multilevel contact
  • Multiscale methods of thermo-viscoelastic frictional contact problems
  • Thermal oxidation processes in semiconductor devices
  • Coupling of surface and subsurface flow
  • Mathematical analysis of multiscale finite element methods for contact
  • Error analysis for multiscale contact problems
  • Mathematical analysis of multiscale boundary methods for contact