A CMA-Simula conference:

Compatible and Innovative Discretizations for Partial Differential Equations

Algorithms, analysis, and implementation on the occasion of Ragnar Winther’s 60th birthday

Time: June 17-19, 2009
Place: Norwegian Academy of Science and Letters, Drammensveien 78, Oslo

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Abstract: The numerical solution of partial differential equations is a fundamental task in science and engineering. Recent research has focused on so-called ‘compatible discretization techniques’, defined as those discretization methods that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum principles. Although this research has established a firm framework for the analysis of discrete PDE problems, most developers and users of scientific software for the numerical solution of PDEs employ simple and less robust methods. With this workshop we aim to bring together researchers on the theoretical aspects of numerical methods and scientists focusing on simulations and software development.

Invited Speakers:

• Wolfgang Bangerth
• Franco Brezzi
• Annalisa Buffa
• Snorre H. Christiansen
• Richard S. Falk
• Ralf Hiptmair
• Robert C. Kirby
• Anders Logg
• Siddhartha Mishra
• Marie Rognes
• Joachim Schöberl
• Xue-Cheng Tai
• Aslak Tveito

Program:

Wednesday 17 June
1:45-2:00   Welcome
2:00-2:45   Richard S. Falk. Title: Bounded cochain projections and approximations of the Hodge Laplacian.
2:45-3:30  Snorre H. Christiansen Title: On the discretization of Yang-Mills-Higgs equations. Abstract.
3:30-4:00   break
4:00-4:45   Xue-Cheng Tai. Title: Nonlinear PDEs on manifold for computer vision. Abstract.

Thursday 18 June
9:00-9:45   Wolfgang Bangerth. Title: Software for (realistic) finite element research. Abstract.
9:45-10:30  Anders Logg. Title: Automated Finite Element Discretization. Abstract.
10:30-11:00 break
11:00-11:45 Robert C. Kirby. Title: Constructing and transforming finite element bases. Abstract.
11:45-1:45  lunch break
1:45-2:30   Aslak Tveito. Title: Computational problems in computing the electrical activity of the heart. Abstract.
2:30-3:30   Contributed talks:

• Trygve Karper Title: Convergent Finite Element methods for viscous compressible Stokes flow. Abstract.
• Holger Heumann Title: Semi-Lagrangian Galerkin methods for Discrete Differential Forms. Abstract.
• Sergey Korotov Title: Discrete maximum principles in the finite element simulations. Abstract.

3:30-4:00   break
4:00-4:45   Siddhartha Mishra Title: Structure preserving algorithms for the Shallow water equations. Abstract.

NB! 6:00 Conference dinner

Friday 19 June
9:00-9:45   Joachim Schöberl. Title: Distributional exact sequences and equilibrated residual a posteriori error estimates. Abstract.
9:45-10:30  Ralf Hiptmair Title: Operator Preconditioning. Abstract.
10:30-11:00 break
11:00-11:45 Marie Rognes Title: Mixed finite element methods for linear viscoelasticity. Abstract.
11:45-1:45  lunch break
1:45-2:30 Annalisa Buffa. Title: New results in IsoGeometric Analysis. Abstract.
2:30-3:30   Contributed talks:

• Gerard Awanou Title: Finite Elements for Symmetric Tensors on Rectangular Meshes. Abstract.
• Pascal Omnes Title: The discrete duality finite volume method. Abstract.
• Artur Palha Title: Spectral Memetic Methods on Quadrilaterals. Abstract.

3:30-4:00   break
4:00-4:45   Franco Brezzi Title: MFD and Nonconforming FEM. Abstract.

Organizers:

• Douglas Arnold, IMA, University of Minnesota, USA
• Helge Galdal, CMA
• Helge Holden, NTNU/CMA
• Hans Petter Langtangen, Simula
• Tom Lyche, CMA
• Kent-André Mardal, Simula
• Marie Rognes, Simula