MTH 656/659: The Finite Element Method for Partial Differential Equations
Spring 2020

Professor: Dr. Vrushali Bokil
Office Hours: W: 4-5pm or by Appt.
Email: Click to email: bokilv at math dot oregonstate dot edu

Course Information

Students should check the CANVAS classpage for general information, announcements, assignments, due dates, and other policies regarding the class.

Class Time : 9:00 am - 9:50 am MWF
Classroom : Remote via Zoom (see CANVAS page for information)
Registration Details:

  • MTH 656: Section 001, CRN 52444
  • MTH 659: Section 001, CRN 53001

Other Links:
Department of Mathematics
Oregon State University
Remote & Online Learning
Zoom, CANVAS Information
Covid-19 News

Disclaimer: Due to the rapid and unprecedented switch to remote education, the instructor, Professor Bokil, reserves the right to make changes to the syllabus throughout the term. Modes of delivery, assessment methods, communication preferences, or other course items might change if we discover the technology does not meet our needs or better ideas emerge. Instructors will do their best to provide ample notice, but students are responsible for checking email regularly and for accommodating course changes.

Prerequisites: Familiarity with numerical methods and graduate standing, or instructor's consent. In addition, familiarity with basic real analysis, differential equations, linear algebra, prior computer programming and partial differential equations (e.g., MTH 453/553) is recommended.

Course Description: This course is an introduction to the finite element method (FEM) for the numerical discretization of partial differential equations (PDEs). Along with finite difference and finite volume methods, FEMs are one of the standard tools for computing numerical solutions to PDE based models that arise in a wide variety of scientific and engineering applications including electromagnetics, solid and structural mechanics, fluid dynamics, acoustics, and thermal conduction.

The FEM is based on the variational formulation of differential equations in Hilbert spaces which gives the method greater flexibility and mathematical elegance. In addition, its ability to deal with complex geometries via unstructured meshes makes it one of the most popular techniques in many branches of engineering.

In this course, students will obtain rigorous training in the basic mathematical and computational aspects of the standard continuous Galerkin FEM. We will cover the basics of the finite element method with particular emphasis on its application to linear elliptic equations in one and two spatial dimensions. Error analysis of the FEM will be an integral part of the course. Programs written in MATLAB will be used to demonstrate examples and students will receive training in writing their own programs. A discussion of available FEM software will also be included, and students will be asked to read papers that describe the implementation of some software packages as well as implement some examples using some of these packages. Some advanced topics from the following set of topics will also be covered, which include mixed FEM, adaptivity, FEM for PDEs involving vector quantities (edge elements), high order FEM, time dependent problems, nonlinear problems.

This course is geared towards graduate students in mathematics, science and engineering including physics, chemistry, oceanography and all engineering disciplines.

Advanced Subjects Sequence MTH 654/5/6
MTH 656 is the third course in the year long sequence MTH 654/5/6 on advanced subjects in numerical analysis. MTH 656 can be taken independently of the others in this sequence.

Learning Outcomes
After successfully completing this class students will:

There is no required textbook for this class. There are a number of excellent textbooks that are available in the Valley Library. These include

MATLAB A scientific programming language is required for this course. MATLAB is preferred due to the integration of computation and visualization, and the fact that the text book authors provide support.

How to Access MATLAB Oregon State University has subscribed to a Total Academic Headcount (TAH) Site License for MATLAB. This new licensing includes many, but not all MATLAB toolboxes. OSU faculty, staff and students can install on up to 4 personally-owned devices or computers. For more information visit Information Services.

Alternative Options to Access MATLAB:

  1. MATLAB via Citrix.
  2. MATLAB Online from a web-browser,
  3. use your phone or tablet on-the-go with MATLAB Mobile.

The following are other options for accessing MATLAB at OSU (currently unavailable):

The following are online resources for learning MATLAB:

Reading Assignments: Look at CANVAS for material covered during each lecture, postings, due dates for assignments, and other information. NOTE: While it may not be stated explicitly each day, students are expected to read assigned material before class. Students are responsible for any material missed due to any absences.

Course Grading and Related Policies:

Important Policies, Regulations and Information:

Students should check this class website and the CANVAS classpage for general information, announcements, assignments, due dates, exam dates and other policies regarding the class.

Makeup Policy: Assignments will have due dates. There will be no makeups given in general. If you are late by one day you can earn upto 75% of the grade of the assignment, late by two days upto 50% of the grade, late by three days, upto 25% of the grade. Beyond three days you will not earn any credit unless there is an exceptional reason such as illness or an emergency. Exceptions can be made by reporting issues to Dr. Bokil. Proper documentation will be needed in order to grant a makeup. Dr. Bokil reserves the right to make all decisions in this regard.

Technology Policy & Unauthorized Recording and Use Policy: I expect that each student will be present and engaged remotely during class time, unless there are circumstances beyond the students control. When remotely present, please refrain from any distracting and inappropriate behavior in the online classroom out of respect for your classmates and your instructor.

Recording and/or dissemination of instructional content (for example, using the camera on your cell phones) is prohibited, unless express permission of the instructor is obtained for an approved accommodation.

Contacting Dr. Bokil: The best way to contact me is via direct email or message through CANVAS. Best place/time for questions is during (remote) office hours. If you are unable to make it to (remote) office hours you may email your questions to me or set up an appointment. Note: Outside of remote class and office hours, questions should be addressed via email. Emails will be answered during working hours between 9am-5pm. Depending on my schedule, emails may not get answered the same day. So please allow 24 hours for a response. I may not be able to answer any homework questions sent via email between 5pm on workdays and 8am the next workday morning, AND between 5pm on Friday and 8am on the subsequent Monday. Please keep this in mind and start working on assignments in a timely manner.

Getting Help: Short questions can be asked during class. Longer questions should be asked during regular (remote) office hours. Appointments can also be made at other times, and you can reach me by email.

Office of Student Life: The Office of Student Life is dedicated to providing educational and developmental opportunities for students to make informed decisions that support their success at Oregon State University. In particular, the following sites will be helpful for you:

  1. Student Ethical Conduct Expectations and Policies: Students are expected to be familiar with Oregon State University’s Statement of Expectations for Student Conduct. Please review and consult material at the following sites.

  2. Statement Regarding Students with Disabilities: Accommodations for students with disabilities are determined and approved by Disability Access Services (DAS). If you, as a student, believe you are eligible for accommodations but have not obtained approval please contact DAS immediately at 541-737-4098 or at Disability Access Services. DAS notifies students and faculty members of approved academic accommodations and coordinates implementation of those accommodations. While not required, students and faculty members are encouraged to discuss details of the implementation of individual accommodations.

  3. Student Care: Many students face difficult times during college; unexpected life events, personal crises, illness or injury, hospitalization, loss of a loved one, and mental health challenges, are examples of challenges that can interfere with college success. Student Care is designed to help students: Learn and understand Oregon State University policies and procedures, Problem-solve within the university and community, Access referrals for personal matters/emergencies.

Reach Out for Success: University students encounter setbacks from time to time. If you encounter difficulties and need assistance, it’s important to reach out. Consider discussing the situation with an instructor or academic advisor. Learn about resources that assist with wellness and academic success at If you are in immediate crisis, please contact the Crisis Text Line by texting OREGON to 741-741 or call the National Suicide Prevention Lifeline at 1-800-273-TALK (8255).

Student Evaluation of Courses: The online Student Evaluation of Teaching system opens to students the Monday of dead week and closes the Monday following the end of finals. Students will receive notification, instructions and the link through their ONID. They may also log into the system via Online Services. Course evaluation results are extremely important and used to help improve courses and the learning experience of future students. Responses are anonymous (unless a student chooses to “sign” their comments agreeing to relinquish anonymity) and unavailable to instructors until after grades have been posted. The results of scaled questions and signed comments go to both the instructor and their unit head/supervisor. Anonymous (unsigned) comments go to the instructor only.

Course Drop/Add and Other Informational Sites: See

  1. OSU Academic Calendar including important add drop dates.
  2. Office of the Registrar
  3. OSU's Grading System
  4. Academic Regulations
  5. Academic Success Center: Remote & Online Learning
  6. Learn@OregonState-Keep Learning
  7. Covid-19 news, resources and updates from OSU Leadership