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. 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.

翻译：本文研究一种新型的一体化计划,以数字方式解决赫森贝格形态中区别指数2的半显性差分位数-位数方程式。 我们的计划为在差数和代数方程式中选择不同的离散性提供了灵活性。 同时,它们的设计将有一个称为变异一致性的属性,即限制的分解性选择决定了拉格兰格乘数的离散性。对于线性制约,我们证明,如果使用片断多元顺序r,则国家命令r+1与乘数的一致。这些结果也将用数字来核实。