An Ultraweak Variational Method for Parameterized Linear Differential-Algebraic Equations

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