Mathematical Theory of Finite Elements 2019

ECCOMAS Advanced Course
Mathematical Theory of Finite Elements

Lecturer: Prof. Leszek Demkowicz
Institute for Computational Engineering and Science (ICES)
The University of Texas at Austin

Venue :
Institute of Fundamental Technological Research
Polish Academy of Sciences
Pawinskiego 5B, 02-106 Warsaw, Poland

Date: 24-28 June 2019

Polish Association for Computational Mechanics (PACM),
Institute of Fundamental Technological Research, Polish Academy of Sciences (IPPT PAN).

Objectives: Review of mathematical theory of the finite element method.

Target group: PhD students, young scientists and all researchers who would like to know and understand mathematical fundamentals of the finite element method.

Scientific/technical areas covered: variational formulations of the finite element method, fundamentals of Galerkin and conforming Finite Element (FE) methods, inf-sup stability condition, fundamentals of the Discontinuous Petrov-Galerkin (DPG) method, application to diffusion-convection-reaction problem.

The participants should register by filling out the REGISTRATION FORM available HERE and send it via email to Dr. Szymon Nosewicz, secretary of PACM by 31 May 2019.
Phone contact: +48 502 236 870

Course fee:
Early payment (before 31 March 2019) 900 PLN,
Regular payment (after 31 March 2019 1000 PLN,
PhD students from IPPT PAN have discount of 100 PLN.
The fee covers the lecture program, coffee breaks and lunches. The fee should be paid by the bank transfer.

Bank transfer information:
Account holder: PTMKM
Account number: 68 1540 1056 2069 6020 7002 0001
Bank name: Bank Ochrony Środowiska S.A.
IBAN: PL 68 1540 1056 2069 6020 7002 0001
Description: ECCOMAS Advanced Course, participant name

All participants are requested to make their own accommodation arrangements, however, a limited number of guests rooms at economic price (180 PLN/day) are available at the course venue.

Course Program
The week-long course consists of three 1.5 hour lectures per day accompanied with a one hour afternoon Q/A discussion session.
Monday, 24 June 2019
1. Classical calculus of variations. Concept of a variational formulation.
2. Diffusion-convection-reaction model problem. Different variational formulations.
3. Distributional derivatives and different energy spaces.
Tuesday, 25 June 2019
1. Abstract framework: vector space, linear and bilinear forms, dual space.
2. Galerkin and Riesz methods.
3. Exact sequence elements.
Wednesday, 26 June 2019
1. Banach Closed Range, Babuška-Nečas, and Babuška Theorems.
2. Coercivity. Lax-Milgram Theorem and Cea’s Lemma.
3. Well posedness of the variational formulations for the model problem.
Thursday, 27 June 2019
1. Mikhlin’s theory of asymptotic stability and convergence.
2. Brezzi’s theory of mixed problems.
3. Concept of optimal test functions.
Friday, 28 June 2019
1. Breaking test spaces and bilinear forms.
2. Fundamentals of the Discontinuous Petrov-Galerkin (DPG) Method.
3. Current research on the DPG method.