Fluid Structure Interaction for Applications in Mathematical Biology.

我预计在本博士课程中可能遇到的主题领域是：(1)非连续Galerkin变分有限元方法；通过允许非协调网格来扩展传统有限元方法。(2)C++编程；编写面向对象的程序代码来实现有限元方法及其任何辅助功能，如报表或绘图输出。(3)科学计算和数值分析；分析有限元方法C++程序得到的结果，包括误差收敛和稳定性。(4)模拟流体流动和流体结构相互作用；预测流体与其约束壁间的作用力的影响。(5)使用多边形单元；在不丢失信息的情况下对固体进行网格划分。(6)后验误差估计的应用；选择特定的单元进行精化以提高计算效率的过程。

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.