Introduction to Finite Element Methods by Krishna Garikipati (U of Michigan)

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source: openmichigan    2014年5月30日
View course on Open.Michigan: http://open.umich.edu/find/open-educa...
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01.01. Introduction, Linear Elliptic Partial Differential Equations (Part 1) 14:47
01.02. Introduction, Linear Elliptic Partial Differential Equations (Part 2) 13:02
01.03. Boundary Conditions 22:19
01.04. Constitutive relations 20:07
01.05. Strong Form of the Partial Differential Equation, Analytic Solution 22:45
01.06. Weak Form of the Partial Differential Equation (Part 1) 12:30
01.07. Weak Form of the Partial Differential Equation (Part 2) 15:06
01.08. Equivalence Between the Strong and Weak Forms (Part 1) 24:21
01.08ct. 1. Intro to C++ (Running Your Code, Basic Structure, Number Types, Vectors) 21:10
01.08ct. 2. Intro to C++ (Conditional Statements, "for" Loops, Scope) 19:28
01.08ct. 3. Intro to C++ (Pointers, Iterators) 14:02
02.01. The Galerkin, or finite dimensional weak form 23:15
02.01. Response to a question 7:29
02.02. Basic Hilbert Spaces (Part 1) 15:52
02.03. Basic Hilbert Spaces (Part 2) 9:29
02.04. FEM for the One Dimensional, Linear Elliptic PDE 22:54
02.04. Response to a question 6:22
02.05. Basis Functions (Part 1) 14:56
02.06. Basis Functions (Part 2) 14:44
02.07. The Bi-Unit Domain (Part 1) 11:45
02.08. The Bi-Unit Domain (Part 2) 16:20
02.09. Finite Dimensional Weak Form as a Sum Over Element Subdomains (Part 1) 16:09
02.10. Finite Dimensional Weak Form as a Sum Over Element Subdomains (Part 2) 12:25
02.10ct. 1. Intro to C++ (Functions) 13:28
02.10ct. 2. Intro to C++ (C++ Classes) 16:44
03.01. The Matrix-Vector Weak Form - I (Part 1) 16:27
03.02. The Matrix-Vector Weak Form - I (Part 2) 17:45
03.03. The Matrix-Vector Weak Form - II (Part 1) 15:38
03.04. The Matrix-Vector Weak Form - II (Part 2) 13:51
03.05. The Matrix-Vector Weak Form - III (Part 1) 22:32
03.06. The Matrix-Vector Weak Form - III (Part 2) 13:23
03.06ct1 Dealii.org, Running Deal.II on a Virtual Machine with Oracle Virtualbox 13:00
03.06ct. 2. Intro to AWS; Using AWS on Windows 24:44
03.06ct2. Correction 3:32
03.06ct. 3. Using AWS on Linux and Mac OS 7:43
03.07. The Final Finite Element Equations in Matrix-Vector form (Part 1) 22:05
03.08. The Final Finite Element Equations in Matrix-Vector form (Part 2) 18:24
03.08. Response to a question 4:36
03.08ct Coding Assignment 1 (main1.cc, Overview of C++ Class in FEM1.h) 19:35
04.01. The Pure Dirichlet Problem (Part 1) 18:16
04.02. The Pure Dirichlet Problem (Part 2) 17:42
04.02. Correction to boardwork 1:01
04.03. Higher Polynomial Order Basis Functions - I 22:56
04.03. Correction to boardwork 0:58
04.04. Higher Polynomial Order Basis Functions - 1 (Part 2) 16:39
04.05. Higher Polynomial Order Basis Functions - II (Part 1) 13:39
04.06. Higher Polynomial Order Basis Functions - III 23:24
04.06ct. Coding Assignment 1 (Functions: Class Constructor to "basis_gradient") 14:41
04.07. The Matrix Vector Equations for Quadratic Basis Functions - I (Part 1) 21:20
04.08. The Matrix Vector Equations for Quadratic Basis Functions - I (Part 2) 11:54
04.09. The Matrix Vector Equations for Quadratic Basis Functions - II (Part 1) 19:10
04.10. The Matrix Vector Equations for Quadratic Basis Functions - II (Part 2) 24:09
04.11. Numerical Integration -- Gaussian Quadrature 13:58
04.11ct. 1. Coding Assignment 1 (Functions: "generate_mesh" to "setup_system") 14:22
04.11ct.2. Coding Assignment 1 (Functions: "assemble_system") 26:59
05.01. Norms (Part 1) 18:23
05.01. Correction to boardwork 0:57
05.01ct. 1. Coding Assignment 1 (Functions: "solve" to "I2norm_of_error") 10:58
05.01ct.2. Visualization Tools 7:18
05.02. Norms (Part 2) 18:22
05.02. Response to a question 5:46
05.03. Consistency of the Finite Element Method 24:28
05.04. The Best Approximation Property 21:33
05.05. The "Pythagorean Theorem" 13:15
05.05. Response to a question 3:32
05.06. Sobolev Estimates and Convergence of the Finite Element Method 23:51
05.07. Finite Element Error Estimates 22:08
06.01. Functionals, Free Energy (Part 1) 17:39
06.02. Functionals, Free Energy (Part 2) 13:21
06.03. Extremization of Functionals 18:31
06.04. Derivation of the Weak Form Using a Variational Principle 20:10
07.01. The Strong Form of Steady State Heat Conduction and Mass Diffusion (Part 1) 18:25
07.02. The Strong Form of Steady State Heat Conduction and Mass Diffusion (Part 2) 19:01
07.02. Response to a question 1:28
07.03. The Strong Form, continued 19:28
07.03. Correction to boardwork 0:43
07.04. The Weak Form 24:34
07.05. The Finite Dimensional Weak Form (Part 1) 12:36
07.06. The Finite Dimensional Weak Form (Part 2) 15:57
07.07. Three-Dimensional Hexahedral Finite Elements 21:31
07.08. Aside: Insight to the Basis Functions by Considering the Two-Dimensional Case 16:44
07.09. Field Derivatives: The Jacobian (Part 1) 12:39
07.10. Field Derivatives: The Jacobian (Part 2) 14:21
07.11. The Integrals in Terms of Degrees of Freedom 16:26
07.12. The Integrals in Terms of Degrees of Freedom - Continued 20:56
07.13. The Matrix-Vector Weak Form (Part 1) 17:20
07.14. The Matrix-Vector Weak Form (Part 2) 11:20
07.15. The Matrix-Vector Weak Form, continued (Part 1) 17:22
07.15. Correction to boardwork 1:01
07.16. The Matrix Vector Weak Form, continued (Part 2) 16:09
07.17. The Matrix-Vector Weak Form, continued further (Part 1) 17:41
07.17. Correction to boardwork 0:48
07.18. The Matrix-Vector Weak Form, continued further (Part 2) 17:19
08.01. Lagrange Basis Functions in 1 Through 3 Dimensions (Part 1) 18:59
08.02. Lagrange Basis Functions in 1 through 3 dimensions (Part 2) 12:37
08.02ct. Coding Assignment 2 (2D Problem) - I 13:34
08.03. Quadrature Rules in 1 Through 3 Dimensions 17:04
08.03ct. 1. Coding Assignment 2 (2D Problem) - II 13:51
08.03ct. 2. Coding Assignment 2 (3D Problem) 6:53
08.04. Triangular and Tetrahedral Elements-Linears (Part 1) 6:52
08.05. Triangular and Tetrahedral Elements Linears (Part 2) 16:30
09.01. The Finite Dimensional Weak Form and Basis Functions (Part 1) 20:40
09.02. The Finite Dimensional Weak Form and Basis Functions (Part 2) 19:13
09.03. The Matrix Vector Weak Form 19:07
09.04. The Matrix Vector Weak Form (Part 2) 9:43
09.04. Correction to boardwork 1:53
10.01. The Strong Form of Linearized Elasticity in Three Dimensions (Part 1) 9:59
10.02. The Strong Form of Linearized Elasticity in Three Dimensions (Part 2) 15:45
10.03 The Strong Form, continued 23:55
10.04. The Constitutive Relations of Linearized Elasticity 21:10
10.05. The Weak Form (Part 1) 17:38
10.05. Response to a Question 7:56
10.06. The Weak Form (Part 2) 20:24
10.07. The Finite-Dimensional Weak Form-Basis Functions (Part 1) 18:24
10.08. The Finite-Dimensional Weak Form-- Basis functions (Part 2) 10:01
10.09. Element Integrals (Part 1) 20:46
10.09. Correction to boardwork 0:54
10.10 Element Integrals (Part 2) 6:46
10.11. The Matrix-Vector Weak Form (Part 1) 19:01
10.12. The Matrix Vector-Weak Form (Part 2) 12:12
10.13. Assembly of the Global Matrix-Vector Equations (Part 1) 20:41
10.14 Assembly of the Global Matrix-Vector Equations II 9:17
10.14. Correction to boardwork 2:54
10.14ct. 1. Coding Assignment 3 - I 10:20
10.14ct. 2. Coding Assignment 3 - II 19:56
10.15 Dirichlet Boundary Conditions (Part 1) 21:24
10.16 Dirichlet Boundary Conditions (Part 2) 14:00
11.01 The Strong Form 16:30
11.01. Correction to boardwork 0:44
11.02 The Weak Form, and Finite Dimensional Weak Form (Part 1) 18:45
11.03 The Weak Form, and Finite Dimensional Weak Form (Part 2) 10:16
11.04. Basis Functions, and the Matrix-Vector Weak Form (Part 1) 19:53
11.04. Correction to Boardwork 0:45
11.05. Basis Functions, and the Matrix-Vector Weak Form (Part 2) 12:04
11.05. Response to a question 0:52
11.06. Dirichlet Boundary Conditions; The Final Matrix Vector Equations 16:58
11.07. Time Discretization; The Euler Family (Part 1) 22:38
11.08. Time Discretization; The Euler Family (Part 2) 9:56
11.09. The V-Form and D-Form 20:55
11.09ct. 1. Coding Assignment 4 - I 11:11
11.09ct. 2. Coding Assignment 4 - II 13:54
11.10. Integration Algorithms for First-Order, Parabolic, Equations-Modal Decomposition (Part 1) 17:25
11.11. Integration Algorithms for First-Order, Parabolic, Equations-Modal Decomposition (Part 2) 12:56
11.12. Modal Decomposition and Modal Equations (Part 1) 16:01
11.13. Modal Decomposition and Modal Equations (Part 2) 16:02
11.14. Modal Equations and Stability of the Time Exact Single Degree of Freedom Systems (Part 1) 10:50
11.15. Modal Equations and Stability of the Time-Exact Single Degree of Freedom Systems (Part 2) 17:39
11.16. Stability of the Time-Discrete Single Degree of Freedom Systems 23:26
11.17. Behavior of Higher-Order Modes; Consistency (Part 1) 18:58
11.18. Behavior of Higher-Order Modes; consistency (Part 2) 19:52
11.19. Convergence (Part 1) 20:50
11.20. Convergence (Part 2) 16:39
12.01. The Strong and Weak Forms 16:38
12.02. The Finite-Dimensional and Matrix-Vector Weak Forms (Part 1) 10:38
12.03. The Finite-Dimensional and Matri-Vector Weak Forms (Part 2) 16:01
12.04. The Time-Discretized Equations 23:16
12.05. Stability (Part 1) 12:58
12.06. Stability (Part 2) 14:36
12.07. Behavior of High-Order Modes 19:33
12.08. Convergence 20:55
13.01. Conclusion, and the Road Ahead 9:26