# Finite Element Method: Variational Methods to Computer Programming

- Institution: IIT Guwahati
- Department: Mechanical Engineering
- Taught by: Prof. Atanu Banerjee, Prof. Arup Nandy
- Level: Undergraduate
- Language: English
- Subjects: Engineering
- Source: [NPTEL](https://nptel.ac.in/courses/112103295)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/112103295)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Lec 1: Functional, First variation, Euler Lagrange equation; Several Dependent variables](https://invisiblenetwork.ai/learn/nptel/112103295/f2bfbb832b48) (YouTube)
2. [Lec 2: Functional with higher order derivatives; Variational statement](https://invisiblenetwork.ai/learn/nptel/112103295/b65db38602c9) (YouTube)
3. [Lec 3: Differential equation, Variational statement and Minimization problem; Rayleigh-Ritz method](https://invisiblenetwork.ai/learn/nptel/112103295/7de1b4e2d6fd) (YouTube)
4. [Lec 4: FEM steps: Explained with discrete linear springs; Gaussian Quadrature rule for integration](https://invisiblenetwork.ai/learn/nptel/112103295/a6ecb8b5798d) (YouTube)
5. [Lec 5: Solving one Ordinary Differential Equation using Linear Finite Element](https://invisiblenetwork.ai/learn/nptel/112103295/e3ccbb9cb25d) (YouTube)
6. [Lec 6: Solving one Ordinary Differential Equation using Quadratic Finite Element](https://invisiblenetwork.ai/learn/nptel/112103295/70863c82675c) (YouTube)
7. [Lec 7: Bar Element: Elemental equation; Matlab Implementation with Example](https://invisiblenetwork.ai/learn/nptel/112103295/fc8bd57d46b4) (YouTube)
8. [Lec 8: Bar Element: Postprocessing; Comparison with Analytical Solution; Bar with linear springs](https://invisiblenetwork.ai/learn/nptel/112103295/e6bb481dd062) (YouTube)
9. [Lec 9: Truss Element: Elemental equation; Matlab Implementation with Example](https://invisiblenetwork.ai/learn/nptel/112103295/4b79369211f7) (YouTube)
10. [Lec 10: Beam Element: Variational statement; Hermite shape function](https://invisiblenetwork.ai/learn/nptel/112103295/d3544710da5a) (YouTube)
11. [Lec 11: Beam Element: Elemental equation; Matlab implementation with Example](https://invisiblenetwork.ai/learn/nptel/112103295/a5a2a3b9bd72) (YouTube)
12. [Lec 12: Beam Element: Matlab implementation for the example with Non-uniform distributed load](https://invisiblenetwork.ai/learn/nptel/112103295/f8ea72f2cf5e) (YouTube)
13. [Lec 13: Frame Element: Derivation of elemental equation in global reference frame](https://invisiblenetwork.ai/learn/nptel/112103295/f74c46e8cd2f) (YouTube)
14. [Lec 14: Frame Element: Matlab implementation with one Example](https://invisiblenetwork.ai/learn/nptel/112103295/e05cfb10458e) (YouTube)
15. [Lec 15: Generalization of Geometry data; Stiffness matrix, Load vector formation at element level](https://invisiblenetwork.ai/learn/nptel/112103295/0ef0f0c1b0df) (YouTube)
16. [Lec 16: Generalization of Assembly, Imposition of Boundary condition and Load information](https://invisiblenetwork.ai/learn/nptel/112103295/bc54a448a8ce) (YouTube)
17. [Lec 17: Indicial Notation: Summation convention, Kronecker delta, Permutation symbol](https://invisiblenetwork.ai/learn/nptel/112103295/5c1933af0843) (YouTube)
18. [Lec 18: Second order tensor; Gradient, Divergence, Curl and Laplacian in Indicial notation](https://invisiblenetwork.ai/learn/nptel/112103295/78f43600969a) (YouTube)
19. [Lec 19: Gauss Divergence theorem and its application in Heat transfer and Structural analysis](https://invisiblenetwork.ai/learn/nptel/112103295/bb8d61a8f4d5) (YouTube)
20. [Lec 20: Derivation of weak form of 2D steady-state heat conduction problem](https://invisiblenetwork.ai/learn/nptel/112103295/141da27e96a9) (YouTube)
21. [Lec 21: Triangular element, calculating element stiffness and element force vector](https://invisiblenetwork.ai/learn/nptel/112103295/1c72ef3b9ca8) (YouTube)
22. [Lec 22: Numerical example, assembly, mapping](https://invisiblenetwork.ai/learn/nptel/112103295/00de6ce6c833) (YouTube)
23. [Lec 23: Numerical integration, Neumann boundary, and higher order shape functions](https://invisiblenetwork.ai/learn/nptel/112103295/7a7a1964aeaf) (YouTube)
24. [Lec 24: Quadrilateral element, Lagrange shape functions, Serendipity elements](https://invisiblenetwork.ai/learn/nptel/112103295/99a86f85e304) (YouTube)
25. [Lec 25: Development of a MATLAB code for solving 2D steady-state heat conduction problem](https://invisiblenetwork.ai/learn/nptel/112103295/8a733bca1160) (YouTube)
26. [Lec 26: Demonstration of the MATLAB code](https://invisiblenetwork.ai/learn/nptel/112103295/bb1ce5321303) (YouTube)
27. [Lec 27: Elasticity problems in two dimension and obtaining the weak form](https://invisiblenetwork.ai/learn/nptel/112103295/76d53dbc5286) (YouTube)
28. [Lec 28: Deriving element stiffness matrix and element force vector, numerical example](https://invisiblenetwork.ai/learn/nptel/112103295/f7b68fe949ec) (YouTube)
29. [Lec 29: Development of a MATLAB code for solving planar elasticity problems](https://invisiblenetwork.ai/learn/nptel/112103295/f56c5b8e59cc) (YouTube)
30. [Lec 30: Superconvergent Patch Recovery, error estimator, adaptive refinement](https://invisiblenetwork.ai/learn/nptel/112103295/143100ec2d0d) (YouTube)
31. [Lec 31: Solving eigenvalue problem in bar and beam, writing FEM code in MATLAB](https://invisiblenetwork.ai/learn/nptel/112103295/f9de15e2b8c5) (YouTube)
32. [Lec 32: Solving eigenvalue problem of membrane, writing FEM code in MATLAB](https://invisiblenetwork.ai/learn/nptel/112103295/eac1b83ddb32) (YouTube)
33. [Lec 33: Solving transient problems (parabolic type)](https://invisiblenetwork.ai/learn/nptel/112103295/98144088bc3c) (YouTube)
34. [Lec 34: Solving transient problems (hyperbolic type)](https://invisiblenetwork.ai/learn/nptel/112103295/45e98f463753) (YouTube)
35. [Lec 35: Solving elasticity problems in 3D using FEM, Solvers](https://invisiblenetwork.ai/learn/nptel/112103295/4fc42300f899) (YouTube)