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 PDE and basic numerical analysis is presented.
 
Element 2 (2.5 credits): Computer lab work.
Implementation of the main numerical methods for PDE, such as finite element methods (FEM) and finite difference methods (FDM), as well as examples of applications to the real problems are treated in mandatory computer sessions. The assignments includes both practical and theoretical exercises.
 

Expected learning outcomes

For a passing grade, the student must be able to

Knowledge and understanding

• formulate a selection of PDE describing physical phenomena
• give a detailed account for the principal differences, strengths and weaknesses of commonly used numerical methods for PDE
• discretize PDE in time and space

Skills

• formulate common numerical solution methods for various PDE with associated boundary/ initial conditions
• derive standard error estimate for finite element and finite difference methods
• develop code for common numerical discretization methods for PDE

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 problem

Required Knowledge

The course requires 22,5 ECTS in calculus including a course in Multivariable Calculus, a course in Linear Algebra, a course in Programming Methodology minimum and a basic course in Numerical Methods. Proficiency in English equivalent to Swedish upper secondary course English 5/A. Where the language of instruction is Swedish, applicants must prove proficiency in Swedish 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 grades is awarded: Fail (U), Pass (3), Pass with merit (4), Pass with distinction (5). For element 2, one of the following grades 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 grade 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.