Go to Course: https://www.coursera.org/learn/finite-element-method
### Course Review: The Finite Element Method for Problems in Physics on Coursera In today's world of engineering and physics, the finite element method (FEM) is a crucial analytical tool that allows professionals to solve complex problems across various domains. For those looking to develop a robust understanding of FEM with a practical coding component, the Coursera course titled **"The Finite Element Method for Problems in Physics"** is an exceptional choice. #### Overview This course provides an in-depth introduction to the finite element method, designed particularly for those in physics and engineering sciences. Spanning approximately **45 hours of lectures**, it comprehensively covers material usually presented in a graduate-level course at a university. While the course emphasizes mathematical concepts, its primary goal is to apply these ideas through coding in a modern, open-source environment. This makes it an invaluable resource for learners who wish to expand their analytical capabilities while gaining hands-on experience. #### Course Syllabus Breakdown The course is structured across **13 units**, each designed to build upon the previous one, creating a cohesive progression of knowledge: 1. **Introduction to One-Dimensional Problems**: Begin with a simple introduction to FEM focusing on one-dimensional cases. 2. **Weak Formulation**: Learn how to approximate the weak form of the problem, facilitating a deeper understanding of FEM principles. 3. **Matrix-Vector Formulation and Coding**: Transition into writing the finite-dimensional weak form in matrix-vector form and get introduced to the deal.ii coding framework. 4. **Boundary Conditions and Higher-Order Functions**: Delve into boundary conditions and higher-order basis functions, preparing for practical coding assignments. 5. **Mathematical Analysis of FEM**: Explore the mathematical foundations of FEM, an essential aspect of accurately applying the method. 6. **Alternate Derivations**: Discover alternative derivations of the weak form that are relevant to various physical problems. 7. **Three-Dimensional Scalar Problems**: Expand your learning to three-dimensional problems, including topics like heat conduction and mass diffusion. 8. **Formulation Details and Coding Assignments**: Complete additional formulation details and undertake the second coding assignment. 9. **Two-Dimensional Formulation**: Shift focus to two-dimensional problems, exploring applications in stability analysis. 10. **Three-Dimensional Elasticity**: Examine three-dimensional, linearized elasticity problems and related coding strategies. 11. **Unsteady Heat Conduction**: Investigate dynamic problems, such as unsteady heat conduction and mass diffusion through finite element methods. 12. **Elastodynamics**: Learn about elastodynamics and its particularities during finite element analysis. 13. **Conclusion and Future Directions**: The course wraps up with suggestions for further study, ensuring students are well-equipped to continue their research or application in FEM. #### Key Highlights - **Clear Structure and Progression**: The course is meticulously structured to guide learners from simple concepts to complex applications. - **Practical Coding Experience**: With an emphasis on coding within the deal.ii framework, students will not only grasp theoretical concepts but also gain the coding proficiency necessary for real-world applications. - **Flexibility and Accessibility**: The use of a modern, open-source environment minimizes barriers to entry, allowing anyone interested in FEM to participate without the need for expensive software licenses. #### Recommendations I highly recommend this course for both students and professionals in physics and engineering interested in enhancing their analytical and computational skills. Whether you are pursuing a graduate degree or looking to expand your understanding of finite element methods, this course offers a solid foundation. ### Conclusion In summary, **"The Finite Element Method for Problems in Physics"** on Coursera is an outstanding course that combines theoretical understanding with practical application. It prepares learners not only to tackle existing problems in physics and engineering but also equips them with the tools to apply FEM in innovative ways across various scientific domains. If you are seeking to elevate your skills in this critical area, this course deserves your consideration.
1
This unit is an introduction to a simple one-dimensional problem that can be solved by the finite element method.
2In this unit you will be introduced to the approximate, or finite-dimensional, weak form for the one-dimensional problem.
3In this unit, you will write the finite-dimensional weak form in a matrix-vector form. You also will be introduced to coding in the deal.ii framework.
4This unit develops further details on boundary conditions, higher-order basis functions, and numerical quadrature. You also will learn about the templates for the first coding assignment.
5This unit outlines the mathematical analysis of the finite element method.
6This unit develops an alternate derivation of the weak form, which is applicable to certain physical problems.
7In this unit, we develop the finite element method for three-dimensional scalar problems, such as the heat conduction or mass diffusion problems.
8In this unit, you will complete some details of the three-dimensional formulation that depend on the choice of basis functions, as well as be introduced to the second coding assignment.
9In this unit, we take a detour to study the two-dimensional formulation for scalar problems, such as the steady state heat or diffusion equations.
10This unit introduces the problem of three-dimensional, linearized elasticity at steady state, and also develops the finite element method for this problem. Aspects of the code templates are also examined.
11In this unit, we study the unsteady heat conduction, or mass diffusion, problem, as well as its finite element formulation.
12In this unit we study the problem of elastodynamics, and its finite element formulation.
13This is a wrap-up, with suggestions for future study.
This course is an introduction to the finite element method as applicable to a range of problems in physics and engineering sciences. The treatment is mathematical, but only for the purpose of clarifying the formulation. The emphasis is on coding up the formulations in a modern, open-source environment that can be expanded to other applications, subsequently. The course includes about 45 hours of lectures covering the material I normally teach in an introductory graduate class at University of
Great class! I truly hope that there are further materials on shell elements, non-linear analysis (geometric nonlinearity, plasticity and hyperelasticity).
Well worth the time if you wish to understand the mathematical origin of the FEM methods used in solving various physical situations such as heat/mass transfer and solid mechanics
Perfect Course !\n\nI recommend it to everyone who is interested in mathematics and physics.
The course was was great. However, illustrative examples solving real engineering problems could be introduced in lecture.
This is the best course as iam learning I so happy about your lecturer's\n\nIt is an wounder full experience that iam getting from you