TY  - JOUR
ID  - Morales2015
LB  - Morales2015
AU  - Morales, Fernando A.
TI  - Notes on the nonlinear dependence of a multiscale coupled system with respect to the interface
ST  - Notes on the nonlinear dependence of a multiscale coupled system with respect to the interface
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2015
VL  - 35
IS  - 4
SP  - 517
EP  - 546
DO  - http://dx.doi.org/10.7494/OpMath.2015.35.4.517
UR  - http://dx.doi.org/10.7494/OpMath.2015.35.4.517
AB  - This work studies the dependence of the solution with respect to interface geometric perturbations, in a multiscaled coupled Darcy flow system in direct variational formulation. A set of admissible perturbation functions and a sense of convergence is presented, as well as sufficient conditions on the forcing terms, in order to conclude strong convergence statements. For the rate of convergence of the solutions we start solving completely the one dimensional case, using orthogonal decompositions on the appropriate subspaces. Finally, the rate of convergence question is analyzed in a simple multi dimensional setting, by studying the nonlinear operators introduced due to the geometric perturbations.
KW  - multiscale coupled systems
KW  - interface geometric perturbations
KW  - variational formulations
KW  - nonlinear dependence
SN  - 1232-9274
ER  -