The virtual course "The Finite Element Method for Physics Problems - Virtual Course - Coursera", is a course with different contents and that offers video classes of Approx. 61 hours to complete. Explore its essential features, and click the orange button to get detailed information on the Coursera e-Learning platform
This course is an introduction to the finite element method applicable to a variety of problems in physics and engineering sciences.
The treatment is mathematical, but only in order to clarify the formulation.
The emphasis is on coding formulations in a modern open source environment that can be expanded to other applications later.
The course includes about 45 hours of lectures covering material I normally teach in an introductory graduate class at the University of Michigan.
The treatment is mathematical, which is natural for a topic whose roots lie deep in functional analysis and variational calculus.
It is not formal, however, because the main objective of these conferences is to turn the viewer into a competent developer of finite element code.
We spend time on rudimentary functional analysis and variational calculus, but this is just to highlight the mathematical basis of the methods, which in turn explains why they work so well.
Much of the success of the finite element method as a computational framework lies in the rigor of its mathematical basis, and this must be appreciated, if only in the elementary way presented here.
A background in PDE and, more importantly, in linear algebra is assumed, although the viewer will find that we developed all the relevant ideas that are needed.
The development itself focuses on the classical forms of partial differential equations (PDEs): elliptic, parabolic, and hyperbolic.
At each stage, however, we make numerous connections to the physical phenomena represented by the PDEs.
For clarity, we start with elliptical PDEs in one dimension (linearized elasticity, steady-state heat conduction, and mass diffusion).
We then move on to three-dimensional elliptical PDEs in scalar unknowns (heat conduction and mass diffusion), before finishing treatment of three-dimensional elliptical PDEs in vector unknowns (linearized elasticity).
Then come parabolic PDEs in three dimensions (unsteady heat conduction and mass diffusion), and the lectures end with hyperbolic PDEs in three dimensions (linear elastodynamics).
Interspersed between the lectures are answers to questions raised by a small group of graduate students and postdoctoral scholars who followed the lectures live.
At appropriate points in the conferences, we break off the mathematical development to design the code framework, which is completely open source and based on C++.
Books: There are many books on finite element methods.
This class does not have a required textbook.
However, we recommend the following books for more detailed and extensive treatments than can be provided in any class form: The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, TJR Hughes, Dover Publications, 2000.
The Finite Element Method: Its Basis and Fundamentals, OC Zienkiewicz, RL Taylor, and JZ Zhu, Butterworth-Heinemann, 2005.
A First Course in Finite Elements, J.
Fish and T.
Belytschko, Wiley, 2007.
Resources: You can download the deal library.
ii on dealii.
org.
The lectures include coding tutorials where we list other resources you can use if you are unable to install deal.
ii on your own computer.
You will need cmake to run deal.
ii.
It is available in cmake.
org.
Linear Static and Dynamic Finite Element Analysis, TJR Hughes, Dover Publications, 2000.
The Finite Element Method: Its Bases and Foundations, OC Zienkiewicz, RL Taylor, and JZ Zhu, Butterworth-Heinemann, 2005.
A first course in finite elements, J.
Fish and T.
Belytschko, Wiley, 2007.
Resources: You can download the deal library.
ii on dealii.
org.
The lectures include coding tutorials where we list other resources you can use if you are unable to install deal.
ii on your own computer.
You will need cmake to run deal.
ii.
It is available in cmake.
org.
Linear Static and Dynamic Finite Element Analysis, TJR Hughes, Dover Publications, 2000.
The Finite Element Method: Its Bases and Foundations, OC Zienkiewicz, RL Taylor, and JZ Zhu, Butterworth-Heinemann, 2005.
A first course in finite elements, J.
Fish and T.
Belytschko, Wiley, 2007.
Resources: You can download the deal library.
ii on dealii.
org.
The lectures include coding tutorials where we list other resources you can use if you are unable to install deal.
ii on your own computer.
You will need cmake to run deal.
ii.
It is available in cmake.
org.
You can download the deal library.
ii on dealii.
org.
The lectures include coding tutorials where we list other resources you can use if you are unable to install deal.
ii on your own computer.
You will need cmake to run deal.
ii.
It is available in cmake.
org.
You can download the deal library.
ii on dealii.
org.
The lectures include coding tutorials where we list other resources you can use if you are unable to install deal.
ii on your own computer.
You will need cmake to run deal.
ii.
It is available in cmake.
org.
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