Lecture 1 - Introduction
Lecture 2 - Introduction to tensors
Lecture 3 - Strong form of differential equations, primary and secondary variables
Lecture 4 - Introduction to variational methods
Lecture 5 - Illustration of variational methods , variational methods of FEM
Lecture 6 - BVP, IVP and IBVP, types of finite elements
Lecture 7 - Weight and shape functions, weak form
Lecture 8 - Domain decomposition
Lecture 9 - Types of boundary conditions, IEN, ID and LM arrays in one-dimension
Lecture 10 - ID and LM arrays in two-dimensions, SDOF and multi-DOF
Lecture 11 - Galerkin weak form of Poisson equation
Lecture 12 - FDM, FVM and FEM
Lecture 13 - FDM and FVM for one-dimensional Poisson equation
Lecture 14 - FEM for one-dimensional Poisson equation
Lecture 15 - FEM using a single bar element
Lecture 16 - Isoparametric elements
Lecture 17 - Illustration for linear bar elements
Lecture 18 - Quadratic bar elements, quadrilateral elements
Lecture 19 - Gauss quadrature for bilinear quadrilateral elements
Lecture 20 - Local coordinates in 2-D, numerical examples
Lecture 21 - Implementation of boundary conditions
Lecture 22 - Implementation of CBC and RBC in 1-D and 2-D
Lecture 23 - Shape functions of linear triangular elements
Lecture 24 - GFEM solution of 2-D Poisson equation of heat conduction - Part 1
Lecture 25 - GFEM solution of 2-D Poisson equation of heat conduction - Part 2
Lecture 26 - Calculation of element level entries of linear triangular elements
Lecture 27 - Solving 2-D Poisson equation using linear triangular elements
Lecture 28 - Classification of linear equation solvers, Gauss elimination
Lecture 29 - Illustration of Thomas algorithm
Lecture 30 - Stationary iterative methods, preconditioning, matrix-free methods
Lecture 31 - Formation of element level matrices and vectors for Parabolic PDE
Lecture 32 - Consistent mass matrix of bar and triangular elements
Lecture 33 - GFEM explicit, implicit and Crank-Nicolson solutions of parabolic PDE in 1-D
Lecture 34 - GFEM for hyperbolic PDEs; first order wave equation, skew-symmetric matrice
Lecture 35 - Galerkin discretized semi-discrete form of the second order wave equation
Lecture 36 - Weak form and fully discrete form of convection-diffusion equation
Lecture 37 - Peclet number, convection and diffusion matrices for bar elements
Lecture 38 - GFEM solution using 2-noded or linear bar elements
Lecture 39 - GFEM solution using 3-noded or quadratic bar elements
Lecture 40 - GFEM explicit solution of 1-D transient convection-diffusion equation
Lecture 41 - Implicit GFEM solution of 1-D unsteady convection-diffusion equation
Lecture 42 - Upwinding and artificial viscosity
Lecture 43 - The Petrov-Galerkin stabilization
Lecture 44 - Petrov-Galerkin weak form of steady convection-diffusion equation
Lecture 45 - Petrov-Galerkin stabilization treatment numerical example
Lecture 46 - Stable Pe limit for convection-diffusion, Navier-stokes equations of motion
Lecture 47 - Coupled and segregated formulations, LBB condition for stable solutions
Lecture 48 - Saddle point problems, inf-sup or LBB compatibility condition, stable elements
Lecture 49 - Connectivity and assembly using Q1Q0 elements for 2-D lid-driven cavity
Lecture 50 - Coupled Galerkin weak form of 2-D, steady Navier-Stokes equations of motion
Lecture 51 - Preprocessor arrays using Q1Q0 element for 2-D Navier-Stokes flow (GFEM)
Lecture 52 - Generation of Q1Q0 element level matrix terms for 2-D Navier-Stokes flow (GFEM)
Lecture 53 - Calculation of x-momentum GFEM matrix for Q1Q0 element
Lecture 54 - Calculation of y-momentum GFEM matrix for Q1Q0 element
Lecture 55 - Calculation of GFEM Stokes flow matrix for Q1Q0 element
Lecture 56 - Implementation of BCs using Q1Q0 elements for 2-D Stokes flow (GFEM)
Lecture 57 - Illustration of assembly using Q1Q0 elements for 2-D Stokes flow (GFEM)
Lecture 58 - The Petrov-Galerkin stabilized Navier-Stokes equations Q1Q1 elements - Part I
Lecture 59 - The Petrov-Galerkin stabilized Navier-Stokes equations Q1Q1 elements - Part II
Lecture 60 - The Petrov-Galerkin stabilized Navier-Stokes equations Q1Q1 elements - Part III
