Continuous Galerkin schemes for semiexplicit differential-algebraic equations

Author:

Altmann Robert1,Herzog Roland2

Affiliation:

1. Department of Mathematics, University of Augsburg, Universitätsstraße 14, 86159 Augsburg, Germany

2. Interdisciplinary Center for Scientific Computing, Heidelberg University, 69120 Heidelberg, Germany

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.

Funder

Deutsche Forschungsgemeinschaft

Publisher

Oxford University Press (OUP)

Subject

Applied Mathematics,Computational Mathematics,General Mathematics

Reference28 articles.

1. Galerkin time-stepping methods for nonlinear parabolic equations;Akrivis;ESAIM Math. Model. Numer. Anal.,2004

2. Regularization and simulation of constrained partial differential equations;Altmann,2015

3. Continuous Galerkin schemes for semi-explicit differential-algebraic equations;Altmann,2021

4. Splitting methods for constrained diffusion–reaction systems;Altmann;Comput. Math. Appl.,2017

5. Runge–Kutta methods for linear semi-explicit operator differential-algebraic equations;Altmann;Math. Comp.,2018

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