Mixed Finite Element Technologies
September 26, 2005 — September 30, 2005
Coordinators:
- Peter Wriggers (Inst. f. Kontinuumsmechanik, Hannover, Germany)
- Carsten Carstensen (Humboldt University Berlin, Berlin, Germany)
Advanced finite element techniques, collected under the name mixed finite element methods, have enormous impact in computational mechanics. Mixed methods provide a tool to solve problems in solid and fluid mechanics in which constraint conditions have to be considered but can also be applied successfully within standard situations.
Examples for such applications are incompressible deformations in elasticity or plasticity or contact problems but also the solution of incompressible Navier-Stokes equations. In the last years considerable progress has been achieved in formulating the mathematical theory and developing associated finite elements for engineering applications. However still open problems exist when mixed methods are applied to nonlinear problems.
In the course different approaches to mixed methods from the engineering and the mathematical point of view will be considered. The special topics of the course range from mathematical foundations of mixed methods in solids, fluids and structures to the engineering applications of the schemes within finite element methods. Emphasis is laid also on the mathematical and numerical treatment of the well known locking phenomenon. Within these topics not only the weak formulations and discretization techniques are considered but also the error analysis of mixed methods with emphasis to modern adaptive mesh-design techniques. Furthermore fast solvers for mixed problems will be discussed as well as new results within the finite element development and discretization schemes for nonlinear engineering applications.