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.
Snorre H. Christiansen
Richard S. Falk
Robert C. Kirby
Wednesday 17 June
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.
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.