Finite Element Applications

During my intensive study of MATLAB's PDE Toolbox documentation (pde.pdf), I encountered several challenging aspects in understanding the provided examples. Although these examples were presented in code format, I found their implementation logic difficult to grasp initially. Consequently, I dedicated one month to systematically analyze each example, ensuring thorough comprehension of the underlying finite element methodologies. Throughout this process, I gained substantial knowledge about finite element applications, including mesh generation techniques, stiffness matrix assembly, boundary condition implementation, and solver configuration. This deep dive not only enhanced my understanding of MATLAB's PDE Toolbox functions like `pdepe` for parabolic-elliptic PDEs and `assembleFEMatrices` for matrix assembly, but also equipped me with the skills to develop sophisticated finite element applications from scratch, incorporating proper discretization strategies and numerical solution techniques.