Modeling dimensionally-heterogeneous problems: analysis, approximation and applications
Friday 5th November 2010
Blanco, Pablo J.; Discacciati, Marco; Quarteroni, Alfio
In the present work a general theoretical framework for coupled dimensionally-heterogeneous partial differential equations is developed. This isdone by recasting the variational formulation in terms of coupling interface variables. In such a general setting we analyze existence and uniqueness of solutions for both the continuous problem and its finite dimensional approximation. This approach also allows the development of different iterative substructuring solution methodologies involving dimensionallyhomogeneous subproblems. Numerical experiments are carried out to test our theoretical results. Keywords: Multiphysics, Heterogeneous PDE models, Augmented formulation,Domain decomposition, Finite elements.