Continuous Galerkin schemes for semiexplicit differential-algebraic equations

Abstract

Abstract This paper studies a new class of integration schemes for the numerical solution of semiexplicit 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. For 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.