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It is an online course which was launched about a year ago. The compelling fact is that it is an absolute successful Massively Open Online Courses (MOOCs).
Finite elements combined with computer programing have made this course an excellent opportunity to be taught as an online course. Important topics like Linear Algebra, partial differential equations on elliptical, parabolic and hyperbolic will be taught in details.
Assessment
This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.
Certification
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Course Credit: Open Michigan
Course Curriculum
| 01.01. Introduction, Linear Elliptic Partial Differential Equations (Part 1) | 00:15:00 | ||
| 01.02. Introduction, Linear Elliptic Partial Differential Equations (Part 2) | 00:13:00 | ||
| 01.03. Boundary Conditions | 00:22:00 | ||
| 01.04. Constitutive relations | 00:20:00 | ||
| 01.05. Strong Form of the Partial Differential Equation, Analytic Solution | 00:23:00 | ||
| 01.06. Weak Form of the Partial Differential Equation (Part 1) | 00:12:00 | ||
| 01.07. Weak Form of the Partial Differential Equation (Part 2) | 00:15:00 | ||
| 01.08. Equivalence Between the Strong and Weak Forms (Part 1) | 00:24:00 | ||
| 01.08ct. 1. Intro to C++ (Running Your Code, Basic Structure, Number Types, Vectors) | 00:21:00 | ||
| 01.08ct. 2. Intro to C++ (Conditional Statements, “for” Loops, Scope) | 00:19:00 | ||
| 01.08ct. 3. Intro to C++ (Pointers, Iterators) | 00:14:00 | ||
| 02.01. The Galerkin, or finite dimensional weak form | 00:23:00 | ||
| 02.01. Response to a question | 00:07:00 | ||
| 02.02. Basic Hilbert Spaces (Part 1) | 00:16:00 | ||
| 02.03. Basic Hilbert Spaces (Part 2) | 00:09:00 | ||
| 02.04. FEM for the One Dimensional, Linear Elliptic PDE | 00:23:00 | ||
| 02.04. Response to a question | 00:06:00 | ||
| 02.05. Basis Functions (Part 1) | 00:15:00 | ||
| 02.06. Basis Functions (Part 2) | 00:15:00 | ||
| 02.07. The Bi-Unit Domain (Part 1) | 00:12:00 | ||
| 02.08. The Bi-Unit Domain (Part 2) | 00:16:00 | ||
| 02.09. Finite Dimensional Weak Form as a Sum Over Element Subdomains (Part 1) | 00:16:00 | ||
| 02.10. Finite Dimensional Weak Form as a Sum Over Element Subdomains (Part 2) | 00:12:00 | ||
| 02.10ct. 1. Intro to C++ (Functions) | 00:13:00 | ||
| 02.10ct. 2. Intro to C++ (C++ Classes) | 00:17:00 | ||
| 03.01. The Matrix-Vector Weak Form – I (Part 1) | 00:16:00 | ||
| 03.02. The Matrix-Vector Weak Form – I (Part 2) | 00:18:00 | ||
| 03.03. The Matrix-Vector Weak Form – II (Part 1) | 00:16:00 | ||
| 03.04. The Matrix-Vector Weak Form – II (Part 2) | 00:14:00 | ||
| 03.05. The Matrix-Vector Weak Form – III (Part 1) | 00:22:00 | ||
| 03.06. The Matrix-Vector Weak Form – III (Part 2) | 00:13:00 | ||
| 03.06ct1 Dealii.org, Running Deal.II on a Virtual Machine with Oracle Virtualbox | 00:13:00 | ||
| 03.06ct. 2. Intro to AWS; Using AWS on Windows | 00:25:00 | ||
| 03.06ct2. Correction | 00:04:00 | ||
| 03.06ct. 3. Using AWS on Linux and Mac OS | 00:08:00 | ||
| 03.07. The Final Finite Element Equations in Matrix-Vector form (Part 1) | 00:22:00 | ||
| 03.08. The Final Finite Element Equations in Matrix-Vector form (Part 2) | 00:18:00 | ||
| 03.08. Response to a question | 00:05:00 | ||
| 03.08ct Coding Assignment 1 (main1.cc, Overview of C++ Class in FEM1.h) | 00:20:00 | ||
| 04.01. The Pure Dirichlet Problem (Part 1) | 00:18:00 | ||
| 04.02. The Pure Dirichlet Problem (Part 2) | 00:18:00 | ||
| 04.02. Correction to boardwork | 00:01:00 | ||
| 04.03. Higher Polynomial Order Basis Functions – I | 00:23:00 | ||
| 04.03. Correction to boardwork | 00:01:00 | ||
| 04.04. Higher Polynomial Order Basis Functions – 1 (Part 2) | 00:17:00 | ||
| 04.05. Higher Polynomial Order Basis Functions – II (Part 1) | 00:14:00 | ||
| 04.06. Higher Polynomial Order Basis Functions – III | 00:23:00 | ||
| 04.06ct. Coding Assignment 1 (Functions: Class Constructor to “basis_gradient”) | 00:15:00 | ||
| 04.07. The Matrix Vector Equations for Quadratic Basis Functions – I (Part 1) | 00:21:00 | ||
| 04.08. The Matrix Vector Equations for Quadratic Basis Functions – I (Part 2) | 00:12:00 | ||
| 04.09. The Matrix Vector Equations for Quadratic Basis Functions – II (Part 1) | 00:19:00 | ||
| 04.10. The Matrix Vector Equations for Quadratic Basis Functions – II (Part 2) | 00:24:00 | ||
| 04.11ct. 1. Coding Assignment 1 (Functions: “generate_mesh” to “setup_system”) | 00:14:00 | ||
| 04.11ct. 1. Coding Assignment 1 (Functions: “generate_mesh” to “setup_system”) | 00:14:00 | ||
| 04.11ct.2. Coding Assignment 1 (Functions: “assemble_system”) | 00:27:00 | ||
| 05.01. Correction to boardwork | 00:01:00 | ||
| 05.01ct. 1. Coding Assignment 1 (Functions: “solve” to “I2norm_of_error”) | 00:11:00 | ||
| 05.01ct.2. Visualization Tools | 00:07:00 | ||
| 05.02. Norms (Part 2) | 00:18:00 | ||
| 05.02. Response to a question | 00:06:00 | ||
| 05.03. Consistency of the Finite Element Method | 00:24:00 | ||
| 05.04. The Best Approximation Property | 00:21:00 | ||
| 05.05. The “Pythagorean Theorem” | 00:13:00 | ||
| 05.05. Response to a question | 00:04:00 | ||
| 05.06. Sobolev Estimates and Convergence of the Finite Element Method | 00:24:00 | ||
| 05.07. Finite Element Error Estimates | 00:22:00 | ||
| 06.01. Functionals, Free Energy (Part 1) | 00:18:00 | ||
| 06.02. Functionals, Free Energy (Part 2) | 00:13:00 | ||
| 06.03. Extremization of Functionals | 00:19:00 | ||
| 06.04. Derivation of the Weak Form Using a Variational Principle | 00:20:00 | ||
| 07.01. The Strong Form of Steady State Heat Conduction and Mass Diffusion (Part 1) | 00:18:00 | ||
| 07.02. The Strong Form of Steady State Heat Conduction and Mass Diffusion (Part 2) | 00:19:00 | ||
| 07.02. Response to a question | 00:01:00 | ||
| 07.03. The Strong Form, continued | 00:19:00 | ||
| 07.03. Correction to boardwork | 00:01:00 | ||
| 07.04. The Weak Form | 00:25:00 | ||
| 07.05. The Finite Dimensional Weak Form (Part 1) | 00:13:00 | ||
| 07.06. The Finite Dimensional Weak Form (Part 2) | 00:16:00 | ||
| 07.07. Three-Dimensional Hexahedral Finite Elements | 00:22:00 | ||
| 07.08. Aside: Insight to the Basis Functions by Considering the Two-Dimensional Case | 00:17:00 | ||
| 07.09. Field Derivatives: The Jacobian (Part 1) | 00:13:00 | ||
| 07.10. Field Derivatives: The Jacobian (Part 2) | 00:14:00 | ||
| 07.11. The Integrals in Terms of Degrees of Freedom | 00:16:00 | ||
| 07.12. The Integrals in Terms of Degrees of Freedom – Continued | 00:21:00 | ||
| 07.13. The Matrix-Vector Weak Form (Part 1) | 00:17:00 | ||
| 07.14. The Matrix-Vector Weak Form (Part 2) | 00:11:00 | ||
| 07.15. The Matrix-Vector Weak Form, continued (Part 1) | 00:17:00 | ||
| 07.15. The Matrix-Vector Weak Form, continued (Part 1) | 00:17:00 | ||
| 07.16. The Matrix Vector Weak Form, continued (Part 2) | 00:16:00 | ||
| 07.17. The Matrix-Vector Weak Form, continued further (Part 1) | 00:18:00 | ||
| 07.17. Correction to boardwork | 00:01:00 | ||
| 07.18. The Matrix-Vector Weak Form, continued further (Part 2) | 00:17:00 | ||
| 07.18 Correction to boardwork | 00:03:00 | ||
| 08.01. Lagrange Basis Functions in 1 Through 3 Dimensions (Part 1) | 00:19:00 | ||
| 08.01 Correction to Boardwork | 00:01:00 | ||
| 08.02. Lagrange Basis Functions in 1 through 3 dimensions (Part 2) | 00:13:00 | ||
| 08.02ct. Coding Assignment 2 (2D Problem) – I | 00:14:00 | ||
| 08.03. Quadrature Rules in 1 Through 3 Dimensions | 00:17:00 | ||
| 08.03ct. 1. Coding Assignment 2 (2D Problem) – II | 00:14:00 | ||
| 08.03ct. 2. Coding Assignment 2 (3D Problem) | 00:15:00 | ||
| 08.04. Triangular and Tetrahedral Elements-Linears (Part 1) | 00:07:00 | ||
| 08.05. Triangular and Tetrahedral Elements Linears (Part 2) | 00:16:00 | ||
| 09.01. The Finite Dimensional Weak Form and Basis Functions (Part 1) | 00:21:00 | ||
| 09.02. The Finite Dimensional Weak Form and Basis Functions (Part 2) | 00:19:00 | ||
| 09.03. The Matrix Vector Weak Form | 00:19:00 | ||
| 09.04. The Matrix Vector Weak Form (Part 2) | 00:09:00 | ||
| 09.04 Correction to boardwork | 00:02:00 | ||
| 10.01. The Strong Form of Linearized Elasticity in Three Dimensions (Part 1) | 00:10:00 | ||
| 10.02. The Strong Form of Linearized Elasticity in Three Dimensions (Part 2) | 00:16:00 | ||
| 10.02 Correction to Boardwork | 00:01:00 | ||
| 10.03 The Strong Form, continued | 00:24:00 | ||
| 10.04. The Constitutive Relations of Linearized Elasticity | 00:21:00 | ||
| 10.05. The Weak Form (Part 1) | 00:18:00 | ||
| 10.05. Response to a Question | 00:08:00 | ||
| 10.06. The Weak Form (Part 2) | 00:20:00 | ||
| 10.07. The Finite-Dimensional Weak Form-Basis Functions (Part 1) | 00:18:00 | ||
| 10.08. The Finite-Dimensional Weak Form– Basis functions (Part 2) | 00:10:00 | ||
| 10.09. Element Integrals (Part 1) | 00:21:00 | ||
| 10.09. Correction to boardwork | 00:01:00 | ||
| 10.10 Element Integrals (Part 2) | 00:07:00 | ||
| 10.11. The Matrix-Vector Weak Form (Part 1) | 00:19:00 | ||
| 10.12. The Matrix Vector-Weak Form (Part 2) | 00:12:00 | ||
| 10.13. Assembly of the Global Matrix-Vector Equations (Part 1) | 00:25:00 | ||
| 10.14 Assembly of the Global Matrix-Vector Equations II | 00:09:00 | ||
| 10.14. Correction to boardwork | 00:34:00 | ||
| 10.14ct. 1. Coding Assignment 3 – I | 00:10:00 | ||
| 10.14ct. 2. Coding Assignment 3 – II | 00:20:00 | ||
| 10.15 Dirichlet Boundary Conditions (Part 1) | 00:21:00 | ||
| 10.16 Dirichlet Boundary Conditions (Part 2) | 00:14:00 | ||
| 11.01 The Strong Form | 00:16:00 | ||
| 11.01. Correction to boardwork | 00:01:00 | ||
| 11.02 The Weak Form, and Finite Dimensional Weak Form (Part 1) | 00:18:00 | ||
| 11.03 The Weak Form, and Finite Dimensional Weak Form (Part 2) | 00:10:00 | ||
| 11.04. Basis Functions, and the Matrix-Vector Weak Form (Part 1) | 00:20:00 | ||
| 11.04. Correction to Boardwork | 00:01:00 | ||
| 11.05. Basis Functions, and the Matrix-Vector Weak Form (Part 2) | 00:12:00 | ||
| 11.05. Response to a question | 00:01:00 | ||
| 11.06. Dirichlet Boundary Conditions; The Final Matrix Vector Equations | 00:17:00 | ||
| 11.07. Time Discretization; The Euler Family (Part 1) | 00:23:00 | ||
| 11.08. Time Discretization; The Euler Family (Part 2) | 00:10:00 | ||
| 11.09. The V-Form and D-Form | 00:21:00 | ||
| 11.09ct. 1. Coding Assignment 4 – I | 00:11:00 | ||
| 11.09ct. 2. Coding Assignment 4 – II | 00:14:00 | ||
| 11.10. Integration Algorithms for First-Order, Parabolic, Equations-Modal Decomposition (Part 1) | 00:17:00 | ||
| 11.11. Integration Algorithms for First-Order, Parabolic, Equations-Modal Decomposition (Part 2) | 00:13:00 | ||
| 11.12. Modal Decomposition and Modal Equations (Part 1) | 00:16:00 | ||
| 11.13. Modal Decomposition and Modal Equations (Part 2) | 00:16:00 | ||
| 11.14. Modal Equations and Stability of the Time Exact Single Degree of Freedom Systems (Part 1) | 00:11:00 | ||
| 11.15. Modal Equations and Stability of the Time-Exact Single Degree of Freedom Systems (Part 2) | 00:18:00 | ||
| 11.16. Stability of the Time-Discrete Single Degree of Freedom Systems | 00:23:00 | ||
| 11.17. Behavior of Higher-Order Modes; Consistency (Part 1) | 00:19:00 | ||
| 11.18. Behavior of Higher-Order Modes; consistency (Part 2) | 00:20:00 | ||
| 11.19. Convergence (Part 1) | 00:21:00 | ||
| 11.20. Convergence (Part 2) | 00:17:00 | ||
| 12.01. The Strong and Weak Forms | 00:18:00 | ||
| 12.02. The Finite-Dimensional and Matrix-Vector Weak Forms (Part 1) | 00:11:00 | ||
| 12.03. The Finite-Dimensional and Matri-Vector Weak Forms (Part 2) | 00:16:00 | ||
| 12.04. The Time-Discretized Equations | 00:23:00 | ||
| 12.05. Stability (Part 1) | 00:13:00 | ||
| 12.06. Stability (Part 2) | 00:15:00 | ||
| 12.07. Behavior of High-Order Modes | 00:19:00 | ||
| 12.08. Convergence | 00:21:00 | ||
| 12.08 Correction to boardwork | 00:03:00 | ||
| 13.01. Conclusion, and the Road Ahead | 00:09:00 | ||
| Assessment | |||
| Submit Your Assignment | 00:00:00 | ||
| Certification | 00:00:00 | ||
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