2013/04/04 by Sina Ober‐Blöbaum, Ober-Blöbaum, Sina, Nils Saake +1 · 2 citations
Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Fluid Dynamics and Vibration Analysis #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1304.1398
openalex publication_date 2013/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work we derive and analyze variational integrators of higher order\nfor the structure-preserving simulation of mechanical systems. The construction\nis based on a space of polynomials together with Gauss and Lobatto quadrature\nrules to approximate the relevant integrals in the variational principle. The\nuse of higher order schemes increases the accuracy of the discrete solution and\nthereby decrease the computational cost while the preservation properties of\nthe scheme are still guaranteed. The order of convergence of the resulting\nvariational integrators are investigated numerically and it is discussed which\ncombination of space of polynomials and quadrature rules provide optimal\nconvergence rates. For particular integrators the order can be increased\ncompared to the Galerkin variational integrators previously introduced in\nMarsden & West 2001. Furthermore, linear stability properties, time\nreversibility, structure-preserving properties as well as efficiency for the\nconstructed variational integrators are investigated and demonstrated by\nnumerical examples.\n