Graduate course on numerical methods for partial differential equations.
Content and learning outcomes
Some topics: finite difference methods, finite element methods, multi grid methods, adaptive methods.
elliptic problems (e.g. diffusion)
parabolic problems (e.g. time-dependent diffusion)
hyperbolic problems (e.g. convection)
systems and nonlinear problems (conservation laws).
Intended learning outcomes
Goal: To understand and use basic methods and theory for numerical solution of partial differential equations, which includes that the student after the course can:
formulate and prove Lax-Milgrams theorem,
formulate, analyze and use multigrid methods,
prove a posteriori and a priori error estimates for elliptic partial differential equations,
prove interpolation error estimates,
formulate and use finite element and finite difference methods for partial differential equations,
formulate and prove Lax equivalence theorem,
use Lax equivalence theorem to analyze finite difference methods,
formulate and use adaptive numerical methods for partial differential equations,
formulate and use symplectic numerical methods for Hamiltonian systems.
Lectures and seminars
Literature and preparations
A Master degree including at least 30 university credits (hp) in in Mathematics (including differential equations and numerical analysis).
- Stig Larsson and Vidar Thomee, Partial Differential Equations with Numerical Methods, Springer-Verlag (2009), ISBN 978-3--540-88705-8, (ST)
- Claes Johnson, Numerical Solution of Partial Differential Equations by the Finite Element Method, Dover Publication (2009), Cambridge University Press (1988) (CJ)
- Adaptive FEM lecture notes (LN1)
- Finite difference methods lecture notes (LN2)
The literature overlaps, so the list gives alternatives.
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
- INL1 - Assignment, 7.5 credits, grading scale: P, F
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
Other requirements for final grade
Home assignments completed
Written exam completed
Opportunity to complete the requirements via supplementary examination
Opportunity to raise an approved grade via renewed examination
- All members of a group are responsible for the group's work.
- In any assessment, every student shall honestly disclose any help received and sources used.
- In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.
Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.Course web FSF3562