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Abstract
This thesis develops strategies for a posteriori error control of discretization and model errors, as well as adaptation strategies, in the context of multiscale finite-element methods. This is done within the general methodology of the DualWeighted Residual Method (DWR). In particular, a reformulation of the Heterogeneous Multiscale Method(HMM) as an abstract model-adaptation framework is introduced that explicitly decouples discretization and model parameters. Based on the framework a samplingadaptation strategy is proposed that allows for simultaneous control of discretization and model errors with the help of classical refinement strategies for mesh and sampling regions. Further, a model-adaptation approach is derived that interprets model adaptivity as a minimization problem of a local model-error indicator.
This allows for the formulation of an efficient post-processing strategy that lifts the requirement of strict a priori knowledge about applicability and quality of effective models. The proposed framework is tested on an elliptic model problem with heterogeneous coefficients, as well as on an advection-diffusion problem with dominant microscopic transport.
Dokumententyp: | Dissertation |
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Erstgutachter: | Rannacher, Prof. Dr. Rolf |
Tag der Prüfung: | 12 Juni 2015 |
Erstellungsdatum: | 01 Jul. 2015 11:17 |
Erscheinungsjahr: | 2015 |
Institute/Einrichtungen: | Fakultät für Mathematik und Informatik > Institut für Mathematik |
DDC-Sachgruppe: | 510 Mathematik |
Normierte Schlagwörter: | Numerical Mathematics, Dual Weighted Residual Method, Multiscale Methods, Model Adaptivity |