TY - GEN
T1 - A new hierarchical model reduction-reduced basis technique for advection-diffusion-reaction problems
AU - Ohlberger, Mario
AU - Smetana, Kathrin
PY - 2012
Y1 - 2012
N2 - We extend previous work on the Hierarchical Model Reduction-Reduced Basis (HMR-RB) approach to an advection-diffusion-reaction problem. In comparison to the Boussinesq approach we do not neglect the dependency on the vertical direction but enhance the solution for the horizontal direction with appropriately chosen basis functions living on the vertical one. This is done by a combination of the frameworks of hierarchical model reduction [4] and the reduced basis methods [3]. We derive a new a posteriori error estimate and demonstrate in numerical experiments that few basis functions suffice to get good approximations.
AB - We extend previous work on the Hierarchical Model Reduction-Reduced Basis (HMR-RB) approach to an advection-diffusion-reaction problem. In comparison to the Boussinesq approach we do not neglect the dependency on the vertical direction but enhance the solution for the horizontal direction with appropriately chosen basis functions living on the vertical one. This is done by a combination of the frameworks of hierarchical model reduction [4] and the reduced basis methods [3]. We derive a new a posteriori error estimate and demonstrate in numerical experiments that few basis functions suffice to get good approximations.
KW - A posteriori error estimation
KW - Adaptive modeling
KW - Hierarchical model reduction
KW - Model reduction
KW - Reduced basis methods
UR - http://www.scopus.com/inward/record.url?scp=84864871424&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84864871424&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:84864871424
SN - 9788493964030
T3 - ECCOMAS Thematic Conference - ADMOS 2011: International Conference on Adaptive Modeling and Simulation, An IACM Special Interest Conference
SP - 343
EP - 354
BT - ECCOMAS Thematic Conference - ADMOS 2011
T2 - 5th International Conference on Adaptive Modeling and Simulation, ADMOS 2011
Y2 - 6 June 2011 through 8 June 2011
ER -