# Introduction to Finite Element Methods

## Video Lectures

Displaying all 140 video lectures.
 Lecture 1 Play Video Introduction, Linear Elliptic Partial Differential Equations (Part 1) Lecture 2 Play Video Introduction, Linear Elliptic Partial Differential Equations (Part 2) Lecture 3 Play Video Boundary Conditions Lecture 4 Play Video Constitutive relations Lecture 5 Play Video Strong Form of the Partial Differential Equation, Analytic Solution Lecture 6 Play Video Weak Form of the Partial Differential Equation (Part 1) Lecture 7 Play Video Weak Form of the Partial Differential Equation (Part 2) Lecture 8 Play Video Equivalence Between the Strong and Weak Forms (Part 1) Lecture 9 Play Video The Galerkin, or finite dimensional weak form Lecture 10 Play Video Response to a question Lecture 11 Play Video Basic Hilbert Spaces (Part 1) Lecture 12 Play Video Basic Hilbert Spaces (Part 2) Lecture 13 Play Video FEM for the One Dimensional, Linear Elliptic PDE Lecture 14 Play Video Response to a question Lecture 15 Play Video Basis Functions (Part 1) Lecture 16 Play Video Basis Functions (Part 2) Lecture 17 Play Video The Bi-Unit Domain (Part 1) Lecture 18 Play Video The Bi-Unit Domain (Part 2) Lecture 19 Play Video Finite Dimensional Weak Form as a Sum Over Element Subdomains (Part 1) Lecture 20 Play Video Finite Dimensional Weak Form as a Sum Over Element Subdomains (Part 2) Lecture 21 Play Video The Matrix-Vector Weak Form - I (Part 1) Lecture 22 Play Video The Matrix-Vector Weak Form - I (Part 2) Lecture 23 Play Video The Matrix-Vector Weak Form - II (Part 1) Lecture 24 Play Video The Matrix-Vector Weak Form - II (Part 2) Lecture 25 Play Video The Matrix-Vector Weak Form - III (Part 1) Lecture 26 Play Video The Matrix-Vector Weak Form - III (Part 2) Lecture 27 Play Video The Final Finite Element Equations in Matrix-Vector form (Part 1) Lecture 28 Play Video The Final Finite Element Equations in Matrix-Vector form (Part 2) Lecture 29 Play Video Response to a question Lecture 30 Play Video The Pure Dirichlet Problem (Part 1) Lecture 31 Play Video The Pure Dirichlet Problem (Part 2) Lecture 32 Play Video Correction to boardwork Lecture 33 Play Video Higher Polynomial Order Basis Functions - I Lecture 34 Play Video Correction to boardwork Lecture 35 Play Video Higher Polynomial Order Basis Functions - 1 (Part 2) Lecture 36 Play Video Higher Polynomial Order Basis Functions - II (Part 1) Lecture 37 Play Video Higher Polynomial Order Basis Functions - III Lecture 38 Play Video The Matrix Vector Equations for Quadratic Basis Functions - I (Part 1) Lecture 39 Play Video The Matrix Vector Equations for Quadratic Basis Functions - I (Part 2) Lecture 40 Play Video The Matrix Vector Equations for Quadratic Basis Functions - II (Part 1) Lecture 41 Play Video The Matrix Vector Equations for Quadratic Basis Functions - II (Part 2) Lecture 42 Play Video Numerical Integration -- Gaussian Quadrature Lecture 43 Play Video Norms (Part 1) Lecture 44 Play Video Correction to boardwork Lecture 45 Play Video Norms (Part 2) Lecture 46 Play Video Response to a question Lecture 47 Play Video Consistency of the Finite Element Method Lecture 48 Play Video The Best Approximation Property Lecture 49 Play Video The "Pythagorean Theorem" Lecture 50 Play Video Response to a question Lecture 51 Play Video Sobolev Estimates and Convergence of the Finite Element Method Lecture 52 Play Video Finite Element Error Estimates Lecture 53 Play Video Functionals, Free Energy (Part 1) Lecture 54 Play Video Functionals, Free Energy (Part 2) Lecture 55 Play Video Extremization of Functionals Lecture 56 Play Video Derivation of the Weak Form Using a Variational Principle Lecture 57 Play Video The Strong Form of Steady State Heat Conduction and Mass Diffusion (Part 1) Lecture 58 Play Video The Strong Form of Steady State Heat Conduction and Mass Diffusion (Part 2) Lecture 59 Play Video Response to a question Lecture 60 Play Video The Strong Form, continued Lecture 61 Play Video Correction to boardwork Lecture 62 Play Video The Weak Form Lecture 63 Play Video The Finite Dimensional Weak Form (Part 1) Lecture 64 Play Video The Finite Dimensional Weak Form (Part 2) Lecture 65 Play Video Three-Dimensional Hexahedral Finite Elements Lecture 66 Play Video Aside: Insight to the Basis Functions by Considering the Two-Dimensional Case Lecture 67 Play Video Field Derivatives: The Jacobian (Part 1) Lecture 68 Play Video Field Derivatives: The Jacobian (Part 2) Lecture 69 Play Video The Integrals in Terms of Degrees of Freedom Lecture 70 Play Video The Integrals in Terms of Degrees of Freedom - Continued Lecture 71 Play Video The Matrix-Vector Weak Form (Part 1) Lecture 72 Play Video The Matrix-Vector Weak Form (Part 2) Lecture 73 Play Video The Matrix-Vector Weak Form, continued (Part 1) Lecture 74 Play Video Correction to boardwork Lecture 75 Play Video The Matrix Vector Weak Form, continued (Part 2) Lecture 76 Play Video The Matrix-Vector Weak Form, continued further (Part 1) Lecture 77 Play Video Correction to boardwork Lecture 78 Play Video The Matrix-Vector Weak Form, continued further (Part 2) Lecture 79 Play Video Correction to boardwork Lecture 80 Play Video Lagrange Basis Functions in 1 Through 3 Dimensions (Part 1) Lecture 81 Play Video Lagrange Basis Functions in 1 through 3 dimensions (Part 2) Lecture 82 Play Video Quadrature Rules in 1 Through 3 Dimensions Lecture 83 Play Video Triangular and Tetrahedral Elements-Linears (Part 1) Lecture 84 Play Video Triangular and Tetrahedral Elements Linears (Part 2) Lecture 85 Play Video The Finite Dimensional Weak Form and Basis Functions (Part 1) Lecture 86 Play Video The Finite Dimensional Weak Form and Basis Functions (Part 2) Lecture 87 Play Video The Matrix Vector Weak Form Lecture 88 Play Video The Matrix Vector Weak Form (Part 2) Lecture 89 Play Video Correction to boardwork Lecture 90 Play Video The Strong Form of Linearized Elasticity in Three Dimensions (Part 1) Lecture 91 Play Video The Strong Form of Linearized Elasticity in Three Dimensions (Part 2) Lecture 92 Play Video The Strong Form, continued Lecture 93 Play Video The Constitutive Relations of Linearized Elasticity Lecture 94 Play Video The Weak Form (Part 1) Lecture 95 Play Video Response to a Question Lecture 96 Play Video The Weak Form (Part 2) Lecture 97 Play Video The Finite-Dimensional Weak Form-Basis Functions (Part 1) Lecture 98 Play Video The Finite-Dimensional Weak Form-- Basis functions (Part 2) Lecture 99 Play Video Element Integrals (Part 1) Lecture 100 Play Video Correction to boardwork Lecture 101 Play Video Element Integrals (Part 2) Lecture 102 Play Video The Matrix-Vector Weak Form (Part 1) Lecture 103 Play Video The Matrix Vector-Weak Form (Part 2) Lecture 104 Play Video Assembly of the Global Matrix-Vector Equations (Part 1) Lecture 105 Play Video Assembly of the Global Matrix-Vector Equations II Lecture 106 Play Video Correction to boardwork Lecture 107 Play Video Dirichlet Boundary Conditions (Part 1) Lecture 108 Play Video Dirichlet Boundary Conditions (Part 2) Lecture 109 Play Video The Strong Form Lecture 110 Play Video Correction to boardwork Lecture 111 Play Video The Weak Form, and Finite Dimensional Weak Form (Part 1) Lecture 112 Play Video The Weak Form, and Finite Dimensional Weak Form (Part 2) Lecture 113 Play Video Basis Functions, and the Matrix-Vector Weak Form (Part 1) Lecture 114 Play Video Correction to Boardwork Lecture 115 Play Video Basis Functions, and the Matrix-Vector Weak Form (Part 2) Lecture 116 Play Video Response to a question Lecture 117 Play Video Dirichlet Boundary Conditions; The Final Matrix Vector Equations Lecture 118 Play Video Time Discretization; The Euler Family (Part 1) Lecture 119 Play Video Time Discretization; The Euler Family (Part 2) Lecture 120 Play Video The V-Form and D-Form Lecture 121 Play Video Integration Algorithms for First-Order, Parabolic, Equations-Modal Decomposition (Part 1) Lecture 122 Play Video Integration Algorithms for First-Order, Parabolic, Equations-Modal Decomposition (Part 2) Lecture 123 Play Video Modal Decomposition and Modal Equations (Part 1) Lecture 124 Play Video Modal Decomposition and Modal Equations (Part 2) Lecture 125 Play Video Modal Equations and Stability of the Time Exact Single Degree of Freedom Systems (Part 1) Lecture 126 Play Video Modal Equations and Stability of the Time-Exact Single Degree of Freedom Systems (Part 2) Lecture 127 Play Video Stability of the Time-Discrete Single Degree of Freedom Systems Lecture 128 Play Video Behavior of Higher-Order Modes; Consistency (Part 1) Lecture 129 Play Video Behavior of Higher-Order Modes; consistency (Part 2) Lecture 130 Play Video Convergence (Part 1) Lecture 131 Play Video Convergence (Part 2) Lecture 132 Play Video The Strong and Weak Forms Lecture 133 Play Video The Finite-Dimensional and Matrix-Vector Weak Forms (Part 1) Lecture 134 Play Video The Finite-Dimensional and Matri-Vector Weak Forms (Part 2) Lecture 135 Play Video The Time-Discretized Equations Lecture 136 Play Video Stability (Part 1) Lecture 137 Play Video Stability (Part 2) Lecture 138 Play Video Behavior of High-Order Modes Lecture 139 Play Video Convergence Lecture 140 Play Video Correction to boardwork