TY - BOOK
T1 - Flux evaluation in primal and dual boundary-coupled problems
AU - Brummelen, van, E.H.
AU - Zee, van der, K.G.
AU - Garg, V.V.
AU - Prudhomme, S.
PY - 2011
Y1 - 2011
N2 - A crucial aspect in boundary-coupled problems such as fluid-structure interaction pertains to the evaluation of fluxes. In boundary-coupled problems, the flux evaluation appears implicitly in the formulation and, consequently, improper flux evaluation can lead to instability. Finite-element approximations of primal and dual problems corresponding to improper formulations can therefore be non-convergent or display suboptimal convergence rates. In this paper, we consider the main aspects of flux evaluation in finite-element approximations of boundary-coupled problems. Based on a model problem, we consider various formulations and illustrate the implications for corresponding primal and dual problems. In addition, we discuss the extension to free-boundary problems, fluid-structure interaction, and electro-osmosis applications.
AB - A crucial aspect in boundary-coupled problems such as fluid-structure interaction pertains to the evaluation of fluxes. In boundary-coupled problems, the flux evaluation appears implicitly in the formulation and, consequently, improper flux evaluation can lead to instability. Finite-element approximations of primal and dual problems corresponding to improper formulations can therefore be non-convergent or display suboptimal convergence rates. In this paper, we consider the main aspects of flux evaluation in finite-element approximations of boundary-coupled problems. Based on a model problem, we consider various formulations and illustrate the implications for corresponding primal and dual problems. In addition, we discuss the extension to free-boundary problems, fluid-structure interaction, and electro-osmosis applications.
M3 - Report
T3 - CASA-report
BT - Flux evaluation in primal and dual boundary-coupled problems
PB - Technische Universiteit Eindhoven
CY - Eindhoven
ER -