Introduction to Finite Element Methods

Video Lectures

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