Mixed methods for the structure-preserving integration in nonlinear structural and elasto-dynamics

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Structure-preserving time-stepping schemes are known to exhibit superior numerical stability and robustness. In particular, the development of energy-momentum schemes was guided by the specific demands of nonlinear structural dynamics. However, these developments have essentially been restricted to displacement-based finite elements. On the other hand mixed finite element formulations are important for many applications.The goal of the present project is to develop a new approach to the design of structure-preserving integrators for mixed finite element formulations. For that purpose a 5-field variational principle shall be used as new pointof departure for the discretization in space and time.The combination of mixed finite elements and structure-preserving schemes promises great advantages with regard to accuracy, numerical stability and robustness. In addition to that, the newly proposed mixed method inspace and time has the potential to significantly extend the applicability of structure-preserving integrators.