# Finite Element Method in Thermal Engineering

- Institution: IIT-ISM Dhanbad
- Department: Mechanical Engineering
- Teacher: Prof. Subhankar Sen
- Level: Undergraduate
- Language: English
- Subjects: Engineering
- Source: [NPTEL](https://nptel.ac.in/courses/112105908)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/112105908)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Lecture -1 : Introduction](https://invisiblenetwork.ai/learn/nptel/112105908/873073216028) (Video)
2. [Lecture -2 : Introduction to tensors](https://invisiblenetwork.ai/learn/nptel/112105908/589bc3a19c62) (Video)
3. [Lecture -3 : Strong form of differential equations, primary and secondary variables](https://invisiblenetwork.ai/learn/nptel/112105908/42dee33da626) (Video)
4. [Lecture -4 : Introduction to variational methods](https://invisiblenetwork.ai/learn/nptel/112105908/d20ff4cc1a59) (Video)
5. [Lecture - 5 : Illustration of variational methods , variational methods of FEM](https://invisiblenetwork.ai/learn/nptel/112105908/6768bda4e5d2) (Video)
6. [Lecture -6 : BVP, IVP and IBVP, types of finite elements](https://invisiblenetwork.ai/learn/nptel/112105908/dafe57a78850) (Video)
7. [Lecture -7 : Weight and shape functions, weak form](https://invisiblenetwork.ai/learn/nptel/112105908/65e74e03784d) (Video)
8. [Lecture -8 : Domain decomposition](https://invisiblenetwork.ai/learn/nptel/112105908/f71367617075) (Video)
9. [Lecture -9: Types of boundary conditions, IEN, ID and LM arrays in one-dimension](https://invisiblenetwork.ai/learn/nptel/112105908/43a870bdff91) (Video)
10. [Lecture -10 : ID and LM arrays in two- dimensions, SDOF and multi-DOF](https://invisiblenetwork.ai/learn/nptel/112105908/c9255e432711) (Video)
11. [Lecture -11 : Galerkin weak form of Poisson equation](https://invisiblenetwork.ai/learn/nptel/112105908/c0f39c51971f) (Video)
12. [Lecture -12 : FDM, FVM and FEM](https://invisiblenetwork.ai/learn/nptel/112105908/03ac721e3a6a) (Video)
13. [Lecture -13 : FDM and FVM for one- dimensional Poisson equation](https://invisiblenetwork.ai/learn/nptel/112105908/b0d020feeed7) (Video)
14. [Lecture -14: FEM for one-dimensional Poisson equation](https://invisiblenetwork.ai/learn/nptel/112105908/814ddf295821) (Video)
15. [Lecture -15 : FEM using a single bar element](https://invisiblenetwork.ai/learn/nptel/112105908/d4d3c1049b84) (Video)
16. [Lecture -16 : Isoparametric elements](https://invisiblenetwork.ai/learn/nptel/112105908/d13292d18ccd) (Video)
17. [Lecture -17 : Illustration for linear bar elements](https://invisiblenetwork.ai/learn/nptel/112105908/6a2a99ecf3d1) (Video)
18. [Lecture -18 : Quadratic bar elements, quadrilateral elements](https://invisiblenetwork.ai/learn/nptel/112105908/b6a5cfaafbfb) (Video)
19. [Lecture -19 : Gauss quadrature for bilinear quadrilateral elements](https://invisiblenetwork.ai/learn/nptel/112105908/9ff29ef96f03) (Video)
20. [Lecture -20 : Local coordinates in 2- D, numerical examples](https://invisiblenetwork.ai/learn/nptel/112105908/6601e1d8632c) (Video)
21. [Lecture -21 : Implementation of boundary conditions](https://invisiblenetwork.ai/learn/nptel/112105908/d518743b8cd3) (Video)
22. [Lecture -22 : Implementation of CBC and RBC in 1-D and 2-D](https://invisiblenetwork.ai/learn/nptel/112105908/2f83a20cd058) (Video)
23. [Lecture -23 : Shape functions of linear triangular elements](https://invisiblenetwork.ai/learn/nptel/112105908/1f55a33d1d66) (Video)
24. [Lecture -24 : GFEM solution of 2-D Poisson equation of heat conduction](https://invisiblenetwork.ai/learn/nptel/112105908/2b2eec2a3043) (Video)
25. [Lecture -25 : GFEM solution of 2-D Poisson equation of heat conduction part 2](https://invisiblenetwork.ai/learn/nptel/112105908/8335de71304f) (Video)
26. [Lecture - 26 : Calculation of element level entries of linear triangular elements](https://invisiblenetwork.ai/learn/nptel/112105908/c9bd0244b74c) (Video)
27. [Lecture 27 : Solving 2-D Poisson equation using linear triangular elements](https://invisiblenetwork.ai/learn/nptel/112105908/b510b41c10a0) (Video)
28. [Lecture -28 : Classification of linear equation solvers, Gauss elimination](https://invisiblenetwork.ai/learn/nptel/112105908/52a371df3886) (Video)
29. [Lecture -29 : Illustration of Thomas algorithm](https://invisiblenetwork.ai/learn/nptel/112105908/b0b146585871) (Video)
30. [Lecture -30 : Stationary iterative methods, preconditioning, matrix-free methods](https://invisiblenetwork.ai/learn/nptel/112105908/3c3656416610) (Video)
31. [Lecture -31 : Formation of element level matrices and vectors for Parabolic PDE](https://invisiblenetwork.ai/learn/nptel/112105908/850214300f0b) (Video)
32. [Lecture -32 : Consistent mass matrix of bar and triangular elements](https://invisiblenetwork.ai/learn/nptel/112105908/eab84b9e4db3) (Video)
33. [Lecture -33 : GFEM explicit, implicit and Crank-Nicolson solutions of parabolic PDE in 1-D](https://invisiblenetwork.ai/learn/nptel/112105908/4fa2ddaa8dc8) (Video)
34. [Lecture -34 : GFEM for hyperbolic PDEs; first order wave equation, skew- symmetric matrice](https://invisiblenetwork.ai/learn/nptel/112105908/7d8ca19fc5d4) (Video)
35. [Lecture -35 : Galerkin discretized semi- discrete form of the second order wave equation](https://invisiblenetwork.ai/learn/nptel/112105908/f2cf4bf0710d) (Video)
36. [Lecture -36 : Weak form and fully discrete form of convection-diffusion equation](https://invisiblenetwork.ai/learn/nptel/112105908/0a722eb2a021) (Video)
37. [Lecture -37 : Peclet number, convection and diffusion matrices for bar elements](https://invisiblenetwork.ai/learn/nptel/112105908/ee2490382cf1) (Video)
38. [Lecture -38 : GFEM solution using 2-noded or linear bar elements](https://invisiblenetwork.ai/learn/nptel/112105908/e307c982d326) (Video)
39. [Lecture-39 : GFEM solution using 3-noded or quadratic bar elements](https://invisiblenetwork.ai/learn/nptel/112105908/fca0a9872dd6) (Video)
40. [Lecture -40 : GFEM explicit solution of 1-D transient convection-diffusion equation](https://invisiblenetwork.ai/learn/nptel/112105908/6361696f0632) (Video)
41. [Lecture -41 : Implicit GFEM solution of 1-D unsteady convection-diffusion equation](https://invisiblenetwork.ai/learn/nptel/112105908/f838dc44b3c3) (Video)
42. [Lecture -42 : Upwinding and artificial viscosity](https://invisiblenetwork.ai/learn/nptel/112105908/9fdbc4566fd3) (Video)
43. [Lecture -43 : The Petrov-Galerkin stabilization](https://invisiblenetwork.ai/learn/nptel/112105908/cf57c5dcfe54) (Video)
44. [Lecture -44 : Petrov-Galerkin weak form of steady convection-diffusion equation](https://invisiblenetwork.ai/learn/nptel/112105908/6f592af73cfd) (Video)
45. [Lecture -45 : Petrov-Galerkin stabilization treatment numerical example](https://invisiblenetwork.ai/learn/nptel/112105908/702048e15727) (Video)
46. [Lecture -46 : Stable Pe limit for convection- diffusion, Navier-stokes equations of motion](https://invisiblenetwork.ai/learn/nptel/112105908/795a42318370) (Video)
47. [Lecture -47 : Coupled and segregated formulations, LBB condition for stable solutions](https://invisiblenetwork.ai/learn/nptel/112105908/00aafe18d50d) (Video)
48. [Lecture - 48 : Saddle point problems, inf-sup or LBB compatibility condition, stable elements](https://invisiblenetwork.ai/learn/nptel/112105908/5af0bd6bcee3) (Video)
49. [Lecture -49 : Connectivity and assembly using Q1Q0 elements for 2-D lid-driven cavity](https://invisiblenetwork.ai/learn/nptel/112105908/e640e02c357e) (Video)
50. [Lecture -50 : Coupled Galerkin weak form of 2-D, steady Navier-Stokes equations of motion](https://invisiblenetwork.ai/learn/nptel/112105908/804cb94249f9) (Video)
51. [Lecture -51 : Preprocessor arrays using Q1Q0 element for 2-D Navier-Stokes flow (GFEM)](https://invisiblenetwork.ai/learn/nptel/112105908/47612301192d) (Video)
52. [Lecture -52 : Generation of Q1Q0 element level matrix terms for 2-D Navier-Stokes flow (GFEM)](https://invisiblenetwork.ai/learn/nptel/112105908/93a698689ac7) (Video)
53. [Lecture -53 : Calculation of x-momentum GFEM matrix for Q1Q0 element](https://invisiblenetwork.ai/learn/nptel/112105908/359d782e01d1) (Video)
54. [Lecture - 54 : Calculation of y-momentum GFEM matrix for Q1Q0 element](https://invisiblenetwork.ai/learn/nptel/112105908/6ffe53f5e606) (Video)
55. [Lecture -55 : Calculation of GFEM Stokes flow matrix for Q1Q0 element](https://invisiblenetwork.ai/learn/nptel/112105908/7e120af1019b) (Video)
56. [Lecture -56 : Implementation of BCs using Q1Q0 elements for 2-D Stokes flow (GFEM)](https://invisiblenetwork.ai/learn/nptel/112105908/f7913868cf96) (Video)
57. [Lecture -57 : Illustration of assembly using Q1Q0 elements for 2-D Stokes flow (GFEM)](https://invisiblenetwork.ai/learn/nptel/112105908/5b60d85ac6bb) (Video)
58. [Lecture -58 : The Petrov-Galerkin stabilized Navier-Stokes equations Q1Q1 elements part I](https://invisiblenetwork.ai/learn/nptel/112105908/af7b2202c2c1) (Video)
59. [Lecture -59 : The Petrov-Galerkin stabilized Navier-Stokes equations Q1Q1 elements part II](https://invisiblenetwork.ai/learn/nptel/112105908/d646e83673dc) (Video)
60. [Lecture -60 : The Petrov-Galerkin stabilized Navier-Stokes equations Q1Q1 elements part III](https://invisiblenetwork.ai/learn/nptel/112105908/ae3e223b2fd8) (Video)