Numerical techniques for the simulation of complex biomechanical processes

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The aim of this project is the research of numerical methods based on an adaptive time-discontinuous Finite Element method for the reliable, robust and efficient computation of nonlinear coupled advection-diffusion-reaction equations.These methods will be tested by application to the complex processes of bone fracture healing. Simultaneously, the model will be enhanced on basis of obtained simulation results. While time-discontinuous Galerkin methods were successfully applied for the monolithic computation of the coupled hyperbolic problem and FIC methods were used for the necessary stabilization of advection-dominated processes in the first phase, adaptively controlled computation techniques based on the gained experiences are to be developed during the second period. Therefore, local enrichments of shape functions (XFEM) based on suitable error indicators are to be designed and tested by application to a model of bone fracture healing.