Directly to content
  1. Publishing |
  2. Search |
  3. Browse |
  4. Recent items rss |
  5. Open Access |
  6. Jur. Issues |
  7. DeutschClear Cookie - decide language by browser settings

Duality-based adaptivity of model and discretization in multiscale finite-element methods

Maier, Matthias Sebastian

[img]
Preview
PDF, English - main document
Download (8MB) | Terms of use

Citation of documents: Please do not cite the URL that is displayed in your browser location input, instead use the DOI, URN or the persistent URL below, as we can guarantee their long-time accessibility.

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.

Item Type: Dissertation
Supervisor: Rannacher, Prof. Dr. Rolf
Date of thesis defense: 12 June 2015
Date Deposited: 01 Jul 2015 11:17
Date: 2015
Faculties / Institutes: The Faculty of Mathematics and Computer Science > Department of Applied Mathematics
Subjects: 510 Mathematics
Controlled Keywords: Numerical Mathematics, Dual Weighted Residual Method, Multiscale Methods, Model Adaptivity
About | FAQ | Contact | Imprint |
OA-LogoDINI certificate 2013Logo der Open-Archives-Initiative