The Finite Element Method for Problems in Physics
Master the finite element method for solving physics problems. Learn theory and coding in C++ for various applications.
Master the finite element method for solving physics problems. Learn theory and coding in C++ for various applications.
This course provides a comprehensive introduction to the finite element method as applied to problems in physics and engineering sciences. The curriculum covers both the mathematical foundations and practical implementation of the method. Students will learn to develop finite element code in a modern, open-source environment, focusing on C++ programming. The course covers a range of topics, including linear elliptic, parabolic, and hyperbolic partial differential equations, with applications to elasticity, heat conduction, and mass diffusion problems in one to three dimensions. The mathematical treatment includes functional analysis and variational calculus to explain the method's effectiveness. Throughout the course, emphasis is placed on connecting the mathematical formulations to physical phenomena. Students will gain hands-on experience through coding assignments, developing skills to analyze and simulate complex physical systems using finite element methods.
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What you'll learn
Understand the mathematical foundations of the finite element method
Develop skills in formulating weak forms for various physical problems
Learn to discretize continuous problems and choose appropriate basis functions
Gain proficiency in C++ programming for finite element implementations
Analyze and solve one-, two-, and three-dimensional problems in elasticity and heat transfer
Master techniques for handling boundary conditions and assembling global systems
Skills you'll gain
This course includes:
29.83 Hours PreRecorded video
12 quizzes
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FullTime access
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There are 13 modules in this course
This course offers an in-depth exploration of the finite element method (FEM) for solving problems in physics and engineering. The curriculum is structured to provide a strong theoretical foundation alongside practical implementation skills. Beginning with one-dimensional elliptic problems, the course progresses to cover three-dimensional scalar and vector problems, including steady-state and transient analyses. Key topics include the formulation of weak forms, discretization techniques, basis functions, and numerical integration. The course emphasizes the mathematical rigor underlying FEM, covering aspects of functional analysis and variational calculus to explain why the method works so well. Students will learn to develop FEM code using C++ and the deal.II library, gaining hands-on experience with real-world applications. The course also covers advanced topics such as error analysis, convergence studies, and time integration schemes for parabolic and hyperbolic problems. By the end of the course, students will have a comprehensive understanding of FEM theory and the skills to implement it for a wide range of physics and engineering problems.
1
Module 1 · 6 Hours to complete
2
Module 2 · 3 Hours to complete
3
Module 3 · 7 Hours to complete
4
Module 4 · 4 Hours to complete
5
Module 5 · 3 Hours to complete
6
Module 6 · 1 Hours to complete
7
Module 7 · 5 Hours to complete
8
Module 8 · 5 Hours to complete
9
Module 9 · 1 Hours to complete
10
Module 10 · 8 Hours to complete
11
Module 11 · 9 Hours to complete
12
Module 12 · 2 Hours to complete
13
Module 13 · 29 Minutes to complete
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Instructor
Computational Scientist & Expert in Mathematical Modeling
Professor Krishna Garikipati, a Professor of Mechanical Engineering and Mathematics at the University of Michigan, is a computational scientist specializing in applied mathematics, nonlinear mechanics, and thermodynamics. His research focuses on mathematical biology, biophysics, and materials physics, exploring tumor growth models, cell mechanics, and phase transformations in structural and battery materials. With a Ph.D. from Stanford University and over two decades at Michigan, he develops physical models, their mathematical forms, numerical methods, and open-source computational tools. Professor Garikipati leads the Coursera course "The Finite Element Method for Problems in Physics," offering insights into mathematical modeling and numerical analysis for real-world physics applications.
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4.6 course rating
544 ratings
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