Special Issue "Modern Finite Element Methods"
A special issue of Mathematics (ISSN 2227-7390).
Deadline for manuscript submissions: closed (30 June 2018).
Interests: scientific computing; finite element methods for fluids; turbulence modelling; optimal shape design; numerical methods for quantitative finance
The numerical approximation of partial differential systems of equations is a very lively field with the Finite Element Method (FEM) at its core, especially with the development of discontinuous Galerkin approximations and a-posteriori error estimations for mesh refinements. Multiscale problems require special finite element methods, such as Xfem, multiscale elements and mimetic methods. Large industrial applications lead also to research on 3-dimensional time dependent problems with uncertainties on the data, optimization and control. For these domain decomposition algorithm and level sets based methods are being investigated and moving mesh techniques, model coupling, sparse grids isoparametric high degree elements and isogeometric elements, to name a few. Finally, any tool which makes the computer implementation easier is a useful research as well; it covers high level dedicated languages like Fenics and FreeFem but also C++ toolboxes or others.
Prof. Dr. Olivier Pironneau
Manuscript Submission Information
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- Innovative Finite Element Method
- Galerkin discontuous methods
- Mimetic methods with polygonal elements
- Time dependent meshes and remeshing
- Iso parametric high degree elements
- Multiscale elements
- Domain decomposition FEM
- Sparse Grid FEM
- Isogeometric elements
- Level sets based FEM optimization
- C++ FEM Toolbox