SF2561 Finita elementmetoden 7,5 hp

The Finite Element Method

En fortsättningskurs om beräkningsmetoder inriktat på finita elementmetoder (FEM) och partiella differentialekvationer.

  • Utbildningsnivå

    Avancerad nivå
  • Huvudområde

    Matematik
    Teknik
  • Betygsskala

    A, B, C, D, E, FX, F

Kurstillfällen/kursomgångar

HT19 för programstuderande

HT19 SAP för Study Abroad Programme (SAP)

  • Perioder

    HT19 P1 (7,5 hp)

  • Anmälningskod

    10045

  • Kursen startar

    2019-08-26

  • Kursen slutar

    2019-10-25

  • Undervisningsspråk

    Engelska

  • Studielokalisering

    KTH Campus

  • Undervisningstid

    Dagtid

  • Undervisningsform

    Normal

  • Antal platser

    Ingen begränsning

  • Planerade moduler

    P1: E1, F1, F2. mer info

  • Kursansvarig

    Sara Zahedi <sara.zahedi@math.kth.se>

  • Lärare

    Sara Zahedi <sara.zahedi@math.kth.se>

  • Målgrupp

    Endast för SAP-studenter. Studenter från UCAS.

  • Anmälan

    Fullfölj anmälan för kursen på antagning.se via denna anmälningslänk.
    Observera att anmälan måste slutföras på antagning.se genom egen inloggning.

HT18 SAP för Study Abroad Programme (SAP)

  • Perioder

    HT18 P1 (7,5 hp)

  • Anmälningskod

    10021

  • Kursen startar

    2018-08-27

  • Kursen slutar

    2018-10-26

  • Undervisningsspråk

    Engelska

  • Studielokalisering

    KTH Campus

  • Undervisningstid

    Dagtid

  • Undervisningsform

    Normal

  • Antal platser

    Ingen begränsning

  • Schema

    Schema (nytt fönster)

  • Planerade moduler

    P1: E1, F1, F2. mer info

  • Kursansvarig

    Sara Zahedi <sara.zahedi@math.kth.se>

  • Lärare

    Sara Zahedi <sara.zahedi@math.kth.se>

  • Målgrupp

    Endast för SAP-studenter. Studenter från UCAS.

HT18 för programstuderande

Lärandemål

Basic laws of nature are typically expressed in the form of partial differential equations (PDE), such as Navier’s equations of elasticity, Maxwell’s equations of electromagnetics,Navier-Stokes equations of fluid flow, and Schrödinger’s equations of quantum mechanics. The Finite element method (FEM) has emerged as a universal tool for the computational solution of PDEs with a multitude of applications in engineering and science. Adaptivity is an important computational technology where the FEM algorithm is automatically tailored to compute a user specified output of interest to a chosen accuracy, to a minimal computational cost.

This FEM course aims to provide the student both with theoretical and practical skills, including the ability to formulate and implement adaptive FEM algorithms for an important family of PDEs.

The theoretical part of this course deals mainly with scalar linear PDE, after which the student will be able to

  • derive the weak formulation
  • formulate a corresponding FEM approximation;
  • estimate the stability of a given linear PDE and it’s FEM approximation;
  • derive a priori and a posteriori error estimates in the energy norm, the L2-norm,
    and linear functionals of the solution;
  • state and use the Lax-Milgram theorem for a given variational problem.

Having completed the practical part of the course the student will be able to:
modify an existing FEM program to solve a new scalar PDE (possibly nonlinear);

  • implement an adaptive mesh refinement algorithm, based on an a posteriori error
  • estimate derived in the theoretical part;
  • describe standard components in FEM algorithms.

Kursens huvudsakliga innehåll

  • FEM-formulation of linear and non-linear partial differential equations, element
    types and their implementation, grid generation, adaption and error control, efficient
    solution algorithms (e.g. by a multigrid method).
  • Applications to stationary and transient diffusion processes, elasticity, convectiondiffusion,
    Navier-Stokes equation, quantum mechanics etc

Behörighet

Single course students: 90 university credits including 45 university credits in Mathematics
or Information Technology. English B, or equivalent.

Rekommenderade förkunskaper

DN2221 Applied Numerical Methods, part 1 (or corresponding), can be read in parallel.

Litteratur

To be announced at least 4 weeks before course start at course web page. Previous year:
K. Eriksson, D. Estep, P. Hansbo, C. Johnson: Computational Differential Equations.
Studentlitteratur, ISBN 91-44-49311-8

Examination

  • LAB2 - Laboration, 4,5, betygsskala: P, F
  • TEN2 - Tentamen, 3,0, betygsskala: A, B, C, D, E, FX, F
  • LAB2 - Laboratory Task, 4.5 credits, grade scale: P, F
  • TEN2 - Examination, 3.0 credits, grade scale: A, B, C, D, E, FX, F

Krav för slutbetyg

  • Examination (TEN2; 3 university credits).
  • Assignments (LAB2; 4.5 university credits).

Ges av

SCI/Matematik

Kontaktperson

Sara Zahedi (sara.zahedi@math.kth.se)

Examinator

Sara Zahedi <sara.zahedi@math.kth.se>

Påbyggnad

Please discuss with the course leader.

Versionsinformation

Kursplan gäller från och med HT2013.
Examinationsinformation gäller från och med HT2013.