Notes on the nonlinear dependence of a multiscale coupled system with respect to the interface
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 th...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AGH Univeristy of Science and Technology Press
2015-01-01
|
| Series: | Opuscula Mathematica |
| Subjects: | |
| Online Access: | http://www.opuscula.agh.edu.pl/vol35/4/art/opuscula_math_3530.pdf |
| _version_ | 1828878494014111744 |
|---|---|
| author | Fernando A. Morales |
| author_facet | Fernando A. Morales |
| author_sort | Fernando A. Morales |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-13T09:06:40Z |
| format | Article |
| id | doaj.art-30f0edbe304941088aadbc5a33cec6ef |
| institution | Directory Open Access Journal |
| issn | 1232-9274 |
| language | English |
| last_indexed | 2024-12-13T09:06:40Z |
| publishDate | 2015-01-01 |
| publisher | AGH Univeristy of Science and Technology Press |
| record_format | Article |
| series | Opuscula Mathematica |
| spelling | doaj.art-30f0edbe304941088aadbc5a33cec6ef2022-12-21T23:53:03ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742015-01-01354517546http://dx.doi.org/10.7494/OpMath.2015.35.4.5173530Notes on the nonlinear dependence of a multiscale coupled system with respect to the interfaceFernando A. Morales0Universidad Nacional de Colombia, Escuela de Matemáticas, Sede Medellín, Calle 59 A No 63-20, Officina 43-106, Medellín, ColombiaThis 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.http://www.opuscula.agh.edu.pl/vol35/4/art/opuscula_math_3530.pdfmultiscale coupled systemsinterface geometric perturbationsvariational formulationsnonlinear dependence |
| spellingShingle | Fernando A. Morales Notes on the nonlinear dependence of a multiscale coupled system with respect to the interface Opuscula Mathematica multiscale coupled systems interface geometric perturbations variational formulations nonlinear dependence |
| title | Notes on the nonlinear dependence of a multiscale coupled system with respect to the interface |
| title_full | Notes on the nonlinear dependence of a multiscale coupled system with respect to the interface |
| title_fullStr | Notes on the nonlinear dependence of a multiscale coupled system with respect to the interface |
| title_full_unstemmed | Notes on the nonlinear dependence of a multiscale coupled system with respect to the interface |
| title_short | Notes on the nonlinear dependence of a multiscale coupled system with respect to the interface |
| title_sort | notes on the nonlinear dependence of a multiscale coupled system with respect to the interface |
| topic | multiscale coupled systems interface geometric perturbations variational formulations nonlinear dependence |
| url | http://www.opuscula.agh.edu.pl/vol35/4/art/opuscula_math_3530.pdf |
| work_keys_str_mv | AT fernandoamorales notesonthenonlineardependenceofamultiscalecoupledsystemwithrespecttotheinterface |