A-Posteriori bounds on linear functionals of coercive 2nd order PDEs using discontinuous Galerkin methods

In this thesis, we extend current capabilities in producing error bounds on the exact linear functionals of linear partial differential equations in a number of ways. Unlike previous approaches, we base our method on the Discontinuous Galerkin finite element method. For equations such as the convection-diffusion equation, the convection term is handled by the standard DG method for hyperbolic problems while the diffusion operator is discretized by the LDG scheme. This choice allows for the effective bounding of outputs associated with high Peclect number problems without resolving all of the details of the solution. In addition to the ability to manage convection dominated problems, we expand the scope of our error bounding algorithm beyond present capabilities to include saddle problems such as the incompressible Stokes equations. Apart from the aforementioned advantages, the DG discretization employed here also produces associated numerical fluxes, which make the complicated "equilibration" procedure that is often necessary in implicit a-posteriori algorithms, unnecessary.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mechanical Engineering

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2006

Author dc:creator

• Wong, Joseph S. H. (Joseph Sze Hsuan)

Advisor dc:contributor.advisor

• Jamie Peraire.

• Mechanical Engineering.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/35624

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/35624