Continuous Galerkin Schemes for Semi-Explicit Differential-Algebraic Equations [article]

Robert Altmann, Roland Herzog
2021 arXiv   pre-print
This paper studies a new class of integration schemes for the numerical solution of semi-explicit differential-algebraic equations of differentiation index 2 in Hessenberg form. Our schemes provide the flexibility to choose different discretizations in the differential and algebraic equations. At the same time, they are designed to have a property called variational consistency, i.e., the choice of the discretization of the constraint determines the discretization of the Lagrange multiplier.
more » ... the case of linear constraints, we prove convergence of order r+1 both for the state and the multiplier if piecewise polynomials of order r are used. These results are also verified numerically.
arXiv:2011.09336v2 fatcat:i3z2uhifirdt5ol3645hledenu