The numerical solution of partial differential equations (PDEs)
is a fundamental task in science and engineering. A necessary requirement
for a numerical scheme is that the discrete solution is close to
the exact solution, i.e., that the scheme converges in a proper
norm with sufficient speed. However, in recent years it has become
clear that for a number of applications certain structure-preserving
discretization schemes are superior to others.
Compatible spatial discretizations can be defined as those that
inherit or mimic fundamental properties of the PDE such as topology,
conservation, symmetries, positivity and maximum principles. Some
of these properties are found among schemes based on: mixed finite
elements , mimetic finite differences, control volume methods, discrete
differential forms, conservative difference schemes, discrete Helmholtz
decompositions , finite integration techniques, staggered grid and
dual grid methods, etc.
In a parallel development, so called "geometric'' techniques
for time-discretization have been developed and shown to be essential
for proper discretization of certain ordinary differential equations
(ODEs). For applications in areas like computational chemistry,
celestial mechanics and particle accelerators the design of special
methods inheriting the variational principles or time-reversing
symmetries of the exact solutions are crucial. Proper time-discretization
leads to methods that preserve Lie group properties of the solution
propagator such as symplecticity, time-reversibility, discrete symmetries,
phase space volume, etc.
A fully compatible approach to time-dependent PDEs should take
both the space and time discretization into consideration. The aim
of this workshop is to serve as a forum where different approaches
to compatible discretizations are presented and compared. The attention
will be given to the identification of the fundamental structures
essential to preserve in a discretization, and the implications
of such properties on stability and accuracy.
Invited presentations are 50 minutes with an additional 10 minutes
of discussion. Contributed Presentations are 25 minutes with an
additional 5 minutes of discussion.
Monday, Sep 26:
10.00-10.05 Ragnar Winther, Director
10.05-11.05 Douglas N. Arnold, University of Minnesota: Differential complexes and mixed finite elements for elasticity.
11.30-12.30 Christian Lubich, University of Tubingen:
Variational approximations in quantum molecular dynamics. Abstract.
14.00-15.00 Ivar Aavatsmark, University of Bergen Control-volume discretizations compatible with physics. Abstract.
14.00-15.30 Elizabeth Mansfield, University of
Kent: Noether's Theorem for smooth, finite difference and finite element
16.00-17.00 Sebastian Reich, Potsdam University:
Multi-scale and conservative time-stepping methods for numerical
weather prediction. Abstract.
Tuesday, Sep 27
09.00-10.00 Franco Brezzi, University of Pavia:
New development in mimetic finite difference methods.
10.30-11.30 Pavel Bochev, Sandia National Laboratories:
Mimetic Discrete Models with Weak Material Laws, or Least Squares
Principles Revisted. Abstract.
11.30-12.30 Hans Munthe Kaas, University of Bergen:
On Group Fourier Analysis and Symmetry Preserving Discretizations
of PDEs. Abstract.
14.00-15.00 Richard S. Falk, Rutgers University: Mixed Finite Elements for Elasticity - a Constructive Approach.
15.00-15.30 Donatella Marini, University of Pavia:
Stabilization mechanisms in discontinuous Galerkin methods.
16.30-17.30 Joachim Schoberl, RICAM Linz: Commuting quasi-interpolation operators for H(curl) and H(div).Abstract.
1900 -> Dinner (information and registration during Monday)
Wednesday, Sep 28
09.00-10.00 Jean-Claude Nédélec,
Ecole Polytechnique: Preconditioning Harmonic Maxwell Integral Equation. Abstract.
10.30-11.00 Snorre Chrstiansen, CMA: On a dual finite element complex.Abstract.
11.00-12.00 Brynjulf Owren, Norwegian University
of Science and Technology: Lie Group Integrators. Abstract.
13.30-14.30 Ivan Yotov, University of Pittsburgh: Relationships between mixed finite element methods, multipoint
flux approximation methods, and mimetic finite difference methods.
15.00-16.00 Claes Johnson, Chalmers, Gøteborg
University Irreversibility in Reversible Systems.Abstract.
Site for workshop, travel description:
CMA / University of Oslo. Visiting address: Moltke Moes vei 35,
(Mathematics building), no 14 on this map.
More detailed travelling description here.
The conference will take place in 12th floor.
Those who will stay at Hotel Gyldenløve, tram line 11 and
19 are passing the hotel in Bogstadveien 20. See tram map here
(leave at 'Vibes gate' stop)
No fee will be charged for participating in the conference. We
are deliberately trying to keep this workshop at a moderate size,
with approximately 40 participants. To request registration send
an email to: Runhild Aae Klausen (runhildk 'at' ifi.uio.no)
by August 25.