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Finite Element Exterior Calculus and Applications

Objective

"The finite element method is one of the most successful techniques for designing numerical methods for systems of partial differential equations (PDEs). It is not only a methodology for developing numerical algorithms, but also a mathematical framework in which to explore their behavior. The finite element exterior calculus (FEEC) provides a new structure that produces a deeper understanding of the finite element method and its connections to the partial differential equation being approximated. The goal is to develop discretizations which are compatible with the geometric, topological, and algebraic structures which underlie well-posedness of the partial differential equation. The phrase FEEC was first used in a paper the PI wrote for Acta Numerica in 2006, together with his coworkers, D.N. Arnold and R.S. Falk. The general philosophy of FEEC has led to the design of new algorithms and software developments, also in areas beyond the direct application of the theory. The present project will be devoted to further development of the foundations of FEEC, and to direct or indirect use of FEEC in specific applications. The ambition is to set the scene for a nubmer of new research directions based on FEEC by giving ground-braking contributions to its foundation. The aim is also to use FEEC as a tool, or a guideline, to extend the foundation of numerical PDEs to a variety of problems for which this foundation does not exist. The more application oriented parts of the project includes topics like numerical methods for elasticity, its generalizations to more general models in materials science such as viscoelasticity, poroelasticity, and liquid crystals, and the applications of these models to CO2 storage and deformations of the spinal cord."

Field of science

  • /natural sciences/computer and information sciences/software/software development
  • /natural sciences/computer and information sciences/software
  • /engineering and technology/materials engineering/crystals
  • /natural sciences/mathematics/pure mathematics/mathematical analysis/differential equations/partial differential equations
  • /engineering and technology/materials engineering/liquid crystal
  • /humanities/philosophy, ethics and religion/philosophy

Call for proposal

ERC-2013-ADG
See other projects for this call

Funding Scheme

ERC-AG - ERC Advanced Grant

Host institution

UNIVERSITETET I OSLO
Address
Problemveien 5-7
0313 Oslo
Norway
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 2 059 687
Principal investigator
Ragnar Winther (Prof.)
Administrative Contact
Yngvar Reichelt (Mr.)

Beneficiaries (1)

UNIVERSITETET I OSLO
Norway
EU contribution
€ 2 059 687
Address
Problemveien 5-7
0313 Oslo
Activity type
Higher or Secondary Education Establishments
Principal investigator
Ragnar Winther (Prof.)
Administrative Contact
Yngvar Reichelt (Mr.)