Chapter 32

Finite Element Method

32.1 Introduction

The last method we will study is by far the most commonly used method in numerical analysis. This method is referred to as finite element method (FEM). It was originally developed for solving problems in solid-state mechanics (plate-bending problems to be more precise), but it has since found wide application in all areas of computational physics and engineering, as well as in CFD. FEM is by far the most flexible method of all methods we have studied so far, and it can be adapted to a wide range of numerical problems. This makes FEM a universal tool for solving differential equations numerically.

The basic concept of FEM can be thought of as splitting the computational domain into individual ...

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