Numerical Methods for PDE

This lecture covers numerical methods for solving Partial Differential Equations (PDEs), focusing on stability, accuracy, and discretization techniques such as Finite Difference Method (FDM), Finite Volume Method (FVM), and Finite Element Method (FEM). It explains the transition from the strong form of PDEs to the weak form, matrix solving, and stiffness matrix calculations. The lecture also delves into nonlinear PDEs, time integration, error control, and micro-Finite Element analysis for bone structures. Additionally, it discusses physics coupling, biomechanical coupling, patient-specific modeling, and the challenges of verification and validation in numerical simulations.