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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

Edukite courses are free to study. To successfully complete a course you must submit all the assignment of the course as part of the assessment. Upon successful completion of a course, you can choose to make your achievement formal by obtaining your Certificate at a cost of £49.

Having an Official Edukite Certification is a great way to celebrate and share your success. You can:

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  • Show it to prove your success

 

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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