Goal-Oriented Error Estimation for Differential-Algebraic Equations
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Differential-algebraic equations (DAEs) arise in many science and engineering applications. However, DAE's have additional complexities (compared to ordinary differential equations) due to the presence of the algebraic constraints, and this in turn effects their error analysis. In this talk we present an adjoint based a posteriori analysis of Hessenberg index 1 and index 2 DAEs. We discuss multiple options for defining the adjoint problem to capture the specific structure of the DAEs, the well-posedness of the adjoint problems, and the corresponding error estimates. Finally, we also present numerical evidence illustrating the performance of the error estimates.