"基础有限元法：从差分法到复杂模型求解"

Finite element method is a computational technique developed based on the principles of finite difference method. In the finite element method, the physical model is discretized and the mesh is not required to be regular, allowing for the use of various types of elements in a mixed manner. This flexibility enables the solution of problems even when equations cannot be formulated. On the other hand, finite difference method involves the division of the grid into regular intervals and the discretization of equations by replacing differentials with differences. It is a method to solve differential equations by representing them as a system of linear equations. Understanding the process of analysis and interpreting the results is crucial in the field of geology as it pertains to practical engineering applications. The weak/Galerkin formulation, finite element space, discretization, boundary treatment, method, and general extensions are important aspects of finite element method, which are discussed in the document "Finite_Elements_Chapter_1.pdf". The document provides an introduction and basic implementation of finite element methods for 1D second order elliptic equations, authored by Xiaoming He from the Department of Mathematics. In summary, finite element method is a powerful computational tool that allows for the discretization of physical models and the solution of complex problems using a mixed mesh of elements. It is a versatile method that complements the finite difference method in solving differential equations and is essential for geologists and engineers in their analysis and interpretation of results in practical applications.