A PDAE formulation of parabolic problems with dynamic boundary conditions
Provides a new theoretical framework for analyzing parabolic problems with dynamic boundary conditions, but the contribution is incremental as it extends existing PDAE approaches to a specific class of problems.
The authors reformulate parabolic problems with dynamic boundary conditions as a partial differential-algebraic equation (PDAE) using a Lagrange multiplier to enforce the coupling condition, and prove well-posedness of the formulation.
The weak formulation of parabolic problems with dynamic boundary conditions is rewritten in form of a partial differential-algebraic equation. More precisely, we consider two dynamic equations with a coupling condition on the boundary. This constraint is included explicitly as an additional equation and incorporated with the help of a Lagrange multiplier. Well-posedness of the formulation is shown.