• Jean-Pierre Croisille, Université de Lorraine
• Matania Ben-Artzi
• Dalia Fishelov

High order approximation methods for biharmonic models are of high interest in numerical mechanics. Two well-known domains of applications are elasticity models and fluid dynamics. The biharmonic operator has played an historic role in these areas. The purpose of this minisymposium is to provide a wide overview of recent developments emerging from the mathematical analysis of biharmonic problems and to attract attention to high order methods for biharmonic problems as a modern branch of mechanics and mathematics.

The emphasis will be on high order numerical methods, recent as well as traditional: Finite element methods, finite difference methods, Discontinuous Galerkin methods, boundary element methods, least square approaches, spline collocation methods, etc.

A particular attention will be devoted to recent developments in the following topics: kernel methods for biharmonic problems, approximation of biharmonic problems in coupled problems, new problems in elasticity theory, Navier-Stokes problems, spectral biharmonic problems, new physical models where biharmonic equations are involved. The mathematical analysis of the approximate solutions, such as stability and convergence, is certainly included in the scope of the proposed minisymposium. Comparative studies of various high order methods (FEM, DG, FD,...), and their analysis is also of interest.

The group of expected participants consists both of senior experts in mechanics and/or numerical mathematics and young researchers and postdocs with a good background in the physical or numerical aspects of this field.