Numerical Analysis of Abstract Differential-Algebraic Equations

The project analyses so called abstract differential algebraic equations (ADAEs). In general, one can describe them as
differential algebraic equations (DAEs) on infinitely dimensional Banach spaces. Such systems arise, for example, from modelling complex processes in the design development of cars or in the electronic circuit design. In the mentioned applications, one achieves coupled systems of partial differential equations (PDEs) and DAEs. The theory and numerical analysis of PDEs and DAEs separately has been made huge progress during the last 20 years. However, oonly a few solvability and convergence results exist for coupled PDE-DAE systems. The project aims the development of a first general class of nonlinear ADAEs for which solvability and convergence can be shown using a Galerkin approach. The focus is directed to systems with operators that have certain monotonicity and smoothness properties.