303 Modern Discretization Methods - Mathematical and Mechanical Aspects

Jörg Schröder, Institute of Mechanics, University Duisburg-Essen, Germany
Peter Wriggers, Institute of Contiuum Mechanics, Leibniz University Hanover, Germany
Advanced numerical simulation techniques for complex problems in solid mechanics are an important field in ongoing research. The developments in many practical computational engineering applications pose great demands on quality, reliability and capability of the applied numerical methods.  Challenges are for example treatment of incompressibility, anisotropy and discontinuities.  Existing computer-based solution methods often provide approximations which cannot guarantee substantial and necessary stability criteria. Especially in the field of geometrical and material non-linearities great challenges exist. Consequently many fundamental questions related to reliable and effective numerical simulations are still open. The "partial'' success of several mixed finite element formulations with focus on the accuracy of all variables motivates new research leading to novel discretization schemes. This and recently discovered surprising advantages of related nonconforming   finite element methods in nonlinear partial differential equations suggest the investigation of mixed and simpler generalized mixed finite element methods such as e.g. discontinuous (Petrov-)Galerkin schemes, least-squares finite element methods or advanced mixed (hybridized) Galerkin methods.

However, there exist many other emerging new schemes which lead to progress in the design of efficient, reliable and robust discretization methods for numerous applications in engineering, biomechanics or material design. The minisymposium is open to new ideas and schemes that describe non-standard numerical methods for solutions in solid mechanics.