AUTHOR=Beurer Emil , Feuerle Moritz , Reich Niklas , Urban Karsten TITLE=An Ultraweak Variational Method for Parameterized Linear Differential-Algebraic Equations JOURNAL=Frontiers in Applied Mathematics and Statistics VOLUME=8 YEAR=2022 URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2022.910786 DOI=10.3389/fams.2022.910786 ISSN=2297-4687 ABSTRACT=

We investigate an ultraweak variational formulation for (parameterized) linear differential-algebraic equations with respect to the time variable which yields an optimally stable system. This is used within a Petrov-Galerkin method to derive a certified detailed discretization which provides an approximate solution in an ultraweak setting as well as for model reduction with respect to time in the spirit of the Reduced Basis Method. A computable sharp error bound is derived. Numerical experiments are presented that show that this method yields a significant reduction and can be combined with well-known system theoretic methods such as Balanced Truncation to reduce the size of the DAE.