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Supported by the Department of Energy.
This workshop is at capacity and closed to further registration.
Organizers:
Douglas N. Arnold
IMA
University of Minnesota
director@ima.umn.edu
http://www.ima.umn.edu/~arnold
Richard B.
Lehoucq
Computational Mathematics and Algorithms Department
Sandia National Laboratories
rblehou@sandia.gov
http://www.cs.sandia.gov/~rlehoucq
Roy A.
Nicolaides
Department of Mathematical Sciences
CarnegieMellon University
dept.head@math.cmu.edu
http://www.math.cmu.edu/people/fac/nicolaides.html
Mikhail
Shashkov
MSB284, Group T7, Theoretical Division
Los Alamos National Laboratory
shashkov@lanl.gov
http://cnls.lanl.gov/~shashkov
Workshop will begin 9:00 AM Tuesday and end by 3:15 PM Saturday. Participants should plan to attend the entire workshop.
The numerical solution of partial differential equations (PDE) is a fundamental task in science and engineering. The goal of the workshop is to bring together a spectrum of scientists at the forefront of the research in the numerical solution of PDEs to discuss compatible spatial discretizations. We define compatible spatial discretizations as those that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum principles. A wide variety of discretization methods applied across a wide range of scientific and engineering applications have been designed to or found to inherit or mimic instrinsic spatial structure and reproduce fundamental properties of the solution of the continuous PDE model at the finite dimensional level. A profusion of such methods and concepts relevant to understanding them have been developed and explored: mixed finite element methods, mimetic finite differences, support operator methods, control volume methods, discrete differential forms, Whitney forms, conservative differencing, discrete Hodge operators, discrete Helmholtz decomposition, finite integration techniques, staggered grid and dual grid methods, etc. This workshop seeks to foster communication among the diverse groups of researchers designing, applying, and studying such methods as well as researchers involved in practical solution of large scale problems that may benefit from advancements in such discretizations; to help elucidate the relations between the different methods and concepts; and to generally advance our understanding in the area of compatible spatial discretization methods for PDE.
Particular points of emphasis will include:




TUESDAY,
MAY 11 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 


8:30  Coffee and Registration  Reception Room EE/CS 3176 

9:15  IMA Directors and Organizers  Welcome and Introduction  
9:30  Douglas
N. Arnold IMA 
Differential Complexes and Stability of Finite Element Methods Slides: pdf 

10:20  

11:00  Roy
Nicolaides Carnegie Mellon University 
Compatible Discretizations, Covolume Algorithms and Differential Forms  
11:50  

1:30  Mikhail
Shashkov Los Alamos National Laboratory 
Slides: pdf 

2:20  

3:00  SECOND CHANCES, i.e., speakers of the day respond to further questions, suggestions, reframe their main points, look toward future directions.  
3:30  
3:40  IMA
Tea and more (Reception and Poster Session) 

WEDNESDAY,
MAY 12 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

9:00  Coffee  Reception Room EE/CS 3176  
9:30  Pavel
Bochev Sandia National Laboratories 
Variational and Geometric Aspects of Compatible Discretizations 

10:20  

11:00  Alain
Bossavit Laboratoire de GÃ©nie Electrique de Paris (LGEP) 

11:50  

1:30  Ralf
Hiptmair Seminar of Applied Mathematics 
Higher
Order Whitney Forms Slides: pdf 

2:20  

3:00  Daniel
A. White Lawrence Livermore National Laboratory 
Development and Application of Compatible Discretizations of Maxwell's Equations Slides: pdf 

4:00  SECOND CHANCES, i.e., speakers of the day respond to further questions, suggestions, reframe their main points, look toward future directions.  
THURSDAY,
MAY
13
All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

9:00  Coffee  Reception Room EE/CS 3176  
9:30  Ivan
Yotov University of Pittsburgh 
Superconvergence in Some Locally Conservative Discretization Methods Slides: pdf 

10:20  

11:00  Thomas
F. Russell National Science Foundation 

11:50  

1:30  Mary
Fanett Wheeler The University of Texas at Austin 
Coupling of MFE or Mimetic Finite Differences with Discontinuous Galerkin for PoroElasticity 

2:20  

3:00  Ivar
Aavatsmark University of Bergen 
MPFA Discretization on Quadrilateral Grids Slides: pdf 

4:00  SECOND CHANCES, i.e., speakers of the day respond to further questions, suggestions, reframe their main points, look toward future directions.  
FRIDAY,
MAY
14
All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

9:00  Coffee  Reception Room EE/CS 3176  
9:30  Eitan
Tadmor University of Maryland, College Park 
Entropy Stability Theory For Difference Approximations of Quasilinear Problems Slides: pdf 

10:20  

11:00  Timothy
J. Barth NASA Ames Research Center 
Entropy Stable FEM Discretization of FirstOrder Systems of Conservation Laws Slides: pdf 

11:50  

1:30  Thomas
J. R. Hughes University of Texas at Austin 

2:20  

3:00  Blair
Perot University of Massachusetts 
Compatible Reconstructions of Vectors and their Application to the NavierStokes Equations 

4:00  SECOND CHANCES, i.e., speakers of the day respond to further questions, suggestions, reframe their main points, look toward future directions.  
6:00  Workshop Dinner  Bona
Vietnamese Restaurant 802 Washington Avenue SE, Minneapolis Phone: 6123315011 

SATURDAY,
MAY
15 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

9:00  Coffee  Reception Room EE/CS 3176  
9:30  Jim
E. Morel Los Alamos National Laboratory 
AsymptoticPreserving Discretization Schemes Slides: pdf 

10:20  

11:00  Daniele
Boffi UniversitÃ di Pavia 
Compatible Discretizations for Eigenvalue Problems Slides: pdf 

11:50  

1:30  Ragnar
Winther University of Oslo, Norway 
From the de Rham Sequence to Mixed Elasticity Slides: pdf 

2:30  SECOND CHANCES, i.e., speakers of the day respond to further questions, suggestions, reframe their main points, look toward future directions.  
3:15 
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