Fluid Structure Interaction for Applications in Mathematical Biology.

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Topic areas I anticipate I would likely encounter in the course of this PhD are:(1) Discontinuous Galerkin variation Finite Element Methods; extending traditional Finite Element Methods by allowing for a non-conforming mesh. (2) C++ programming; writing object oriented program code to implement the Finite Element Methods together with any supporting functions such as report or plot output.(3) Scientific computation and numerical analysis; analysing results obtained from the Finite Element Method C++ program including error convergence and stability.(4) Modelling fluid flow and fluid structure interaction; predicting the effects of forces exerted between the fluids and their restraining walls.(5) Use of polytope elements; applying meshes to solids without losing information.(6) Application of a-posteriori error estimation; process of selecting particular elements for refinement to improve computational efficiency.