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Dates (SS2015)

The lecture has been held in SS 2015 at TU Wien.

Lecturer: Christoph Lehrenfeld

Poster, TISS, organisational notes (updated), lecture notes

Further information: Prof. Dr. Joachim Schöberl

First meeting: Tue, 3. Mar, 15:00 13:30 , Besprechungszimmer 3. Stock (vis a vis SR 101B)

Lecture+Exercise: Thursday 16:00 - 18:30, Besprechungszimmer 3. Stock (vis a vis SR 101B)


In the lecture modern numerical methods for the discretization of interface problems are presented. Partial differential equations the solution of which has (weak) discontinuities across given interfaces require special care for their numerical treatment. The concept of extended finite element methods (XFEM) introduces finite element spaces which provide ansatz functions which are discontinuous across the interface. Based on this approach the XFEM is used for different applications. We will present interface problems arising in two-phase flow applications and discuss their numerical solution. The lecture includes

  • the introduction of XFEM,
  • the discussion of implementational aspects
  • and their numerical analysis.

The students will work on a student project. Presentation of the problem setting and their solution is part of the course.

Student projects

The Trace FEM for PDEs on surfaces

Project report by T.Jawecki, M. Wess

A fictitious domain method for an osmosis problem

Project report by M. Hochsteger, C. Lackner, L. Kogler

Two-phase Stokes with velocity/pressure XFEM

Project report by P. Lederer, C. Pfeiler, C. Wintersteiger

convergence of Stokes-XFEM

XFEM discretization of a stationary Stefan problem

Project report by A. Rieder, M. Ruggeri , B. Stiftner

solution of Stefan problem

Exercise material / Netgen/NGSolve tutorials

Debian packages for Netgen-6.1-dev and NGSolve-6.1-dev

Exercise schedule / content

  • Notes on how to get started with the installation of Netgen/NGSolve, html, pdf
  • March, 12th - 26th, 2015: Introduction to Netgen/NGSolve:
    • Using Netgen/NGSolve for a simple poisson problem, html, pdf
    • A second example with Netgen/NGSolve, html, pdf
    • Programming with NGSolve, Introduction using MyLittleNGSolve html, pdf, slides
    • Programming with NGSolve, Implementing a (Two-Phase) Stokes problem html, pdf, slides
  • April, 16th-23th, 2015: Introduction to Netgen/NGSolve/NGSxfem
    • Using the additional library ngsxfem to solve (simple) xfem problems html, pdf, slides
    • Programming with ngsxfem

Other sources for learning to deal with Netgen/NGSolve

Lecture material / literature

Organisational notes:

Lecture notes will be created during the semester.

  • Lecture notes (last update: June, 4th, 2015), pdf

Further reading (on which the lecture notes are also based):

  • Sven Groß, Arnold Reusken, Numerical Methods for Two-Phase incompressible flows, Springer textbook
  • Christoph Lehrenfeld, On a Space-Time Extended Finite Element Method for the Solution of a Class of Two-Phase Mass Transport Problems, Ph.D. thesis, RWTH Aachen, 2015, pdf(A4), pdf(A5)