论文标题
连续的Galerkin方案，用于半明确的差异代数方程
Continuous Galerkin Schemes for Semi-Explicit Differential-Algebraic Equations
论文作者
论文摘要
本文研究了一类新的集成方案，用于Hessenberg形式的分化指数2的半阐释差分差异方程的数值解。我们的方案提供了在差分方程和代数方程中选择不同离散化的灵活性。同时，它们被设计为具有称为变分的一致性的属性，即，约束的离散化选择决定了Lagrange乘数的离散化。对于线性约束的情况，如果使用阶r的分段多项式，我们证明了状态和乘数的顺序r+1的收敛性。这些结果也会通过数值验证。
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.
