Large time-stepping is important for efficient long-time simulations of deterministic and stochastic Hamiltonian dynamical systems. Conventional structure-preserving integrators, while being successful generic systems, have limited tolerance to time step size due stability accuracy constraints. We propose use data innovate classical integrators so that they can be adaptive large are tailored ea...

We present a formulation of rigid body dynamics with frictional contact that leverages ideas from discrete mechanics to derive time-stepping schemes with any desired order of integration accuracy. By utilizing the new time-stepping methods as dynamics constraints in a direct trajectory optimization scheme, we are able to perform contact-implicit trajectory optimization with accuracy equal to tr...

Abstract This article is concerned with the discretisation of Stokes equations on time-dependent domains in an Eulerian coordinate framework. Our work can be seen as extension a recent paper by Lehrenfeld and Olshanskii (ESAIM: M2AN 53(2):585–614, 2019), where BDF-type time-stepping schemes are studied for parabolic equation moving domains. For space discretisation, geometrically unfitted finit...

In this paper, we design and study two modifications of the first order standard pressure increment projection scheme for the Stokes system. The first scheme improves the existing schemes in the case of open boundary condition by modifying the pressure increment boundary condition, thereby minimizing the pressure boundary layer and recovering the optimal first order decay. The second scheme all...

In this contribution, we deal with time-stepping schemes for geometrically nonlinear multiplicative elasto-plasto-dynamics. Thereby, the approximation in space as well as in time rely both on a Finite Element approach, providing a general framework which conceptually includes also higher-order schemes. In this context, the algorithmic conservation properties of the related integrators strongly ...