A-Posteriori bounds on linear functionals of coercive 2nd order PDEs using discontinuous Galerkin methods
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76272525-MIT.pdf
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d41985bd219fe4351ce08c21eb05656e
Author(s)
Wong, Joseph S. H. (Joseph Sze Hsuan)
Advisor(s)
Jamie Peraire.
Date Issued
2006
Publisher
Massachusetts Institute of Technology
Abstract
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.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2006.
Includes bibliographical references (p. 127-132).
Subjects
Mechanical Engineering.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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