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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.

4.6

(544 ratings)

69,093 already enrolled

English

پښتو, বাংলা, اردو, 3 more

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The Finite Element Method for Problems in Physics

This course includes

61 Hours

Of Self-paced video lessons

Intermediate Level

Completion Certificate

awarded on course completion

2,435

Audit For Free

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

finite element method
numerical analysis
partial differential equations
C++ programming
computational physics
engineering simulations
elasticity
heat conduction

This course includes:

29.83 Hours PreRecorded video

12 quizzes

Access on Mobile, Tablet, Desktop

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

Fee Structure

Payment options

Financial Aid

Instructor

Krishna Garikipati, Ph.D.
Krishna Garikipati, Ph.D.

4.7 rating

60 Reviews

69,764 Students

1 Course

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.

The Finite Element Method for Problems in Physics

This course includes

61 Hours

Of Self-paced video lessons

Intermediate Level

Completion Certificate

awarded on course completion

2,435

Audit For Free

Testimonials

Testimonials and success stories are a testament to the quality of this program and its impact on your career and learning journey. Be the first to help others make an informed decision by sharing your review of the course.

4.6 course rating

544 ratings

Frequently asked questions

Below are some of the most commonly asked questions about this course. We aim to provide clear and concise answers to help you better understand the course content, structure, and any other relevant information. If you have any additional questions or if your question is not listed here, please don't hesitate to reach out to our support team for further assistance.