Computational Sciences Theme

Short Course on hp-Finite Element Methods

April 19-21, 2006

Department of Mathematics, University of Reading

Lecturer: Prof. Jens Markus Melenk

Vienna University of Technology


[Introduction] [Programme] [Accommodation] [Further Information]

Introduction

Professor Melenk has an outstanding international reputation for his research in computational mathematics, especially for his work on hp finite element methods (hp-FEM) and for work on meshfree methods. Indicators of this international reputation are his many high quality research outputs (two of his papers from the late nineties have over 240 citations each), his many invitations to speak at prestigious international meetings, and his recent appointment to a chair in Vienna.

Professor Melenk is an LMS visiting fellow. During his stay, he will also give a seminar at Oxford University (April 20, 2pm) and at Imperial College (April 25, 3pm)

The course is sponsored by the Computational Sciences Theme of the University of Reading.

Course content:

The hp-version of the finite element method (hp-FEM) is a generalisation of the classical (h-version) FEM and the p-version FEM/spectral method in that convergence is achieved by simultaneously refining the mesh and increasing the approximation order. For elliptic problems with piecewise analytic data, which is the case arising in practice, the hp-FEM based on the appropriate mesh refinement strategy can lead to exponential convergence. The course will cover theoretical and practical issues of the hp-FEM. On the theoretical side, the course will clarify the role of the so-called ``geometric mesh'', which is really the key to the exponential convergence. Since many important features of the hp-FEM can already be understood in one-dimensional problems, the course will start with this simple setting before discussing the extensions to higher dimensions. On the practical side, the course will address the question of setting up the system matrix (``stiffness matrix'') and the design of preconditioners for the resulting linear system of equations. We will discuss in particular the so-called ``sum factorisation'' technique, which is one of the most important methods to speeding up the generation of the system matrix. The preconditioners presented will be of domain decomposition type. It is planned to briefly address issues arising when leaving the H^1-elliptic setting. The Stokes equations may serve as an example. There, the hp-discretisations have to be selected such that the Galerkin method is stable, i.e., the discretisations of the velocity and pressure field are suitably linked.

Programme

(ALL LECTURES IN ROOM 113 MATHS)

April 19

12-1 Lecture 1 [[Lunch break]]

2-3 Lecture 2 [[Coffee Break]]

3:30-5 Problem session

April 20

9-10 Lecture 3 [[Coffee break]]

10:30-11:30 Lecture 4 [[Lunch break]]

2-3:30 Problem session [[Coffee Break]]

4:00-5:00 Guest Lecture: Dr E. Hannert (Reading)

April 21

10-11 Lecture 5 [[Coffee break]]

11:30-12:30 Lecture 6 [[Lunch break]]

2-4 Problem session [[Coffee Break]]

Accommodation

Accommodation can been arranged in ensuite rooms at Whiteknights Hall, on the university campus. The cost is of GBP 39.95 per night.

In addition to accommodation, breakfast and dinner can be provided at Whiteknights Hall for course residents.

Coffee breaks will be provided for course participants.

Registration

The course is free, but you should register by sending an e-mail to the organiser, Dr. Beatrice Pelloni,
b.pelloni@rdg.ac.uk

Interested participant are strongly encouraged to express their interest informally to the organiser as soon as possible.

Further Information

Further information available from:

Dr. Beatrice Pelloni
Department of Mathematics
University of Reading
Reading RG6 6AX
Tel. +44 (0)118 3788990
b.pelloni@rdg.ac.uk.

Page last modified: 7 February, 2006