Ask AI: Which method does what – Finite Volumes (FV), Finite Differences (FD), Finite Elements (FE)?

Finite Volume Method (FV): FV is an approach for solving partial differential equations, which divides the domain into a set of discrete cells or volumes. This method is commonly used for approximation of conservation laws, such as in computational fluid dynamics. Finite Difference Method (FD): FD is a method of approximating solutions to differential equations, and is used to solve a wide range of problems. It is based on the idea of replacing a continuous problem with a sequence of discrete approximations. Finite Element Method (FE): FE is a numerical technique for solving engineering problems. This method is based on breaking down a complex problem into smaller, simpler, and more manageable pieces. The method uses a numerical process and then combines the results to determine the overall solution.