Numerical Methods for Partial Differential Equations, 7.5 Credits

Contents

The course consists of two parts

Element 1 (5 credits): Theory.
The course provides an overview of numerical methods for solving partial differential equations (PDE). The most common methods are derived in detail for various PDEs and basic numerical analyses are presented.
 
Element 2 (2.5 credits): Computer lab work.
Implementation of the main numerical methods for PDEs, such as finite element methods (FEM) and finite difference methods (FDM), as well as examples of applications in real problems are treated in mandatory computer sessions. The assignments include both practical and theoretical exercises.
 

Expected learning outcomes

For a passing grade, the student must be able to

Knowledge and understanding

• critically account for a selection of PDEs describing physical phenomena
• give a detailed account for the principal differences, strengths and weaknesses of commonly used numerical methods for PDE

Skills

• apply common numerical solution methods for various PDEs with associated boundary/ initial conditions
• discretize PDEs in space and time
• derive standard error estimates for finite element and finite difference methods
• develop programming codes for common numerical discretization methods for PDEs

Judgement and approach

• present and critically discuss solution methods and results in written reports
• select appropriate numerical methods based on the characteristics of a PDE problems

Required Knowledge

The course requires 90 ECTS including 22,5 ECTS in Calculus including a course in Multivariable Calculus, a course in Linear Algebra, a course in Programming Methodology and a basic course in Numerical Methods. Proficiency in English and Swedish equivalent to the level required for basic eligibility for higher studies.

Form of instruction

The teaching in element 1 takes the form of lectures and lessons. The teaching in element 2 takes the form of lab work.

Examination modes

Element 1 is assessed through a written examination. Element 2 is assessed through written lab reports. For element 1, one of the following judgemensts is awarded: Fail (U), Pass (3), Pass with merit (4), Pass with distinction (5). For element 2, one of the following judgements is awarded: Fail (U), or Pass (G). For the course as whole, one of the following grades is awarded: Fail (U), Pass (3), Pass with merit (4), Pass with distinction (5). The grade for the whole course is determined by the judgement given for element 1. To pass the whole course, all elements must have been passed. The grade is only set once all compulsory elements have been assessed.

A student who has been awarded a passing grade for the course cannot be reassessed for a higher grade. Students who do not pass a test or examination on the original date are given another date to retake the examination. A student who has sat two examinations for a course or a part of a course, without passing either examination, has the right to have another examiner appointed, provided there are no specific reasons for not doing so (Chapter 6, Section 22, HEO). The request for a new examiner is made to the Head of the Department of Mathematics and Mathematical Statistics. Examinations based on this course syllabus are guaranteed to be offered for two years after the date of the student's first registration for the course.

Credit transfer
All students have the right to have their previous education or equivalent, and  their working life experience evaluated for possible consideration in the corresponding education at Umeå university. Application forms should be adressed to Student services/Degree evaluation office. More information regarding credit transfer can be found on the student web pages of Umeå university, http://www.student.umu.se, and in the Higher Education Ordinance (chapter 6). If denied, the application can be appealed (as per the Higher Education Ordinance, chapter 12) to Överklagandenämnden för högskolan. This includes partially denied applications

Other regulations

This course can not be included in a degree together with another course with similar contents. When in doubt, the student should consult the director of study at the department of mathematics and mathematical statistics. The course can also be included in the subject area of computational science and engineering.