Duality-based adaptive finite element methods with application to time-dependent problems
2010 (English)Doctoral thesis, comprehensive summary (Other academic)
To simulate real world problems modeled by differential equations, it is often not sufficient to consider and tackle a single equation. Rather, complex phenomena are modeled by several partial dierential equations that are coupled to each other. For example, a heart beat involve electric activity, mechanics of the movement of the walls and valves, as well as blood fow - a true multiphysics problem. There may also be ordinary differential equations modeling the reactions on a cellular level, and these may act on a much finer scale in both space and time. Determining efficient and accurate simulation tools for such multiscalar multiphysics problems is a challenge.
The five scientific papers constituting this thesis investigate and present solutions to issues regarding accurate and efficient simulation using adaptive finite element methods. These include handling local accuracy through submodeling, analyzing error propagation in time-dependent multiphysics problems, developing efficient algorithms for adaptivity in time and space, and deriving error analysis for coupled PDE-ODE systems. In all these examples, the error is analyzed and controlled using the framework of dual-weighted residuals, and the spatial meshes are handled using octree based data structures. However, few realistic geometries fit such grid and to address this issue a discontinuous Galerkin Nitsche method is presented and analyzed.
Place, publisher, year, edition, pages
Umeå: Institutionen för matematik och matematisk statistik, Umeå universitet , 2010. , 37 p.
Doctoral thesis / Umeå University, Department of Mathematics, ISSN 1102-8300 ; 45
finite element methods, dual-weighted residual method, multiphysics, a posteriori error estimation, adaptive algorithms, discontinuous Galerkin
Research subject Mathematics
IdentifiersURN: urn:nbn:se:umu:diva-33872ISBN: 978-91-7459-023-4OAI: oai:DiVA.org:umu-33872DiVA: diva2:318503
2010-06-10, MIT-huset, MA121, Umeå universitet, Umeå, 10:15 (English)
Houston, Paul, Professor
Larson, Mats G., Professor
List of papers