Finite element method | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-10-04

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Finite_element_method


00:01:11 1 Basic concepts
00:05:55 2 History
00:08:56 3 Technical discussion
00:09:06 3.1 The structure of finite element methods
00:11:16 3.2 Illustrative problems P1 and P2
00:15:40 3.3 Weak formulation
00:15:56 3.3.1 The weak form of P1
00:20:18 3.3.2 The weak form of P2
00:22:45 3.3.3 A proof outline of existence and uniqueness of the solution
00:25:35 4 Discretization
00:27:56 4.1 For problem P1
00:30:33 4.2 For problem P2
00:32:41 4.3 Choosing a basis
00:38:31 4.4 Small support of the basis
00:42:48 4.5 Matrix form of the problem
00:52:05 4.6 General form of the finite element method
00:56:22 5 Various types of finite element methods
00:56:33 5.1 AEM
00:56:50 5.2 Generalized finite element method
00:57:35 5.3 Mixed finite element method
00:57:58 5.4 hp-FEM
00:58:20 5.5 hpk-FEM
00:58:46 5.6 XFEM
01:00:37 5.7 Scaled boundary finite element method (SBFEM)
01:01:26 5.8 S-FEM
01:01:50 5.9 Spectral element method
01:02:19 5.10 Meshfree methods
01:02:28 5.11 Discontinuous Galerkin methods
01:02:38 5.12 Finite element limit analysis
01:02:48 5.13 Stretched grid method
01:02:57 5.14 Loubignac iteration
01:03:12 6 Link with the gradient discretisation method
01:03:51 7 Comparison to the finite difference method
01:06:13 8 Application
01:08:56 9 See also



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SUMMARY
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The finite element method (FEM) is a numerical method for solving problems of engineering and mathematical physics. Typical problem areas of interest include structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The  analytical solution of these problems generally require the solution to boundary value problems for partial differential equations. The finite element method formulation of the problem results in a system of algebraic equations. The method approximates the unknown function over the domain. To solve the problem, it subdivides a large system into smaller, simpler parts that are called finite elements. The simple equations that model these finite elements are then assembled into a larger system of equations that models the entire problem. FEM then uses variational methods from the calculus of variations to approximate a solution by minimizing an associated error function.
Studying or analyzing a phenomenon with FEM is often referred to as finite element analysis (FEA).