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The aim of the PhD project is to study a novel integrated model reduction mesh adaptation approach for nonlinear advection-dominated systems of partial differential equations (PDEs), notably aerodynamic and hydraulic flows.

To this aim, registration-based model reduction will be combined with parametric mesh adaptation. Registration-based model reduction relies on a parametric mapping to identify and then track relevant features of the solution field. Parametric mesh adaptation refers to the task of determining an accurate mesh for a range of system configurations. This should lead to considerably more parsimonious discretizations compared to uniform refinement, for any target accuracy.

The PhD student is expected to develop, analyze and then implement the combined model-reduction mesh-adaptation procedure for nonlinear advection-dominated PDEs.