- Title Information
- Title
- Wave Resolution Properties and Weighted Essentially Non-Oscillatory Limiter for Discontinuous Galerkin Methods
- Name:
Personal
- Name Part
- Zhong, Xinghui
- Role
- Role Term:
Text
- creator
- Origin Information
- Copyright Date
- 2012
- Physical Description
- Extent
- xvii, 122 p.
- digitalOrigin
- born digital
- Note
- Thesis (Ph.D. -- Brown University (2012)
- Name:
Personal
- Name Part
- Shu, Chi-Wang
- Role
- Role Term:
Text
- Director
- Name:
Personal
- Name Part
- Guzman, Johnny
- Role
- Role Term:
Text
- Reader
- Name:
Personal
- Name Part
- Hesthaven, Jan
- Role
- Role Term:
Text
- Reader
- Name:
Corporate
- Name Part
- Brown University. Applied Mathematics
- Role
- Role Term:
Text
- sponsor
- Genre (aat)
- theses
- Subject
- Topic
- discontinuous Galerkin method
- Subject
- Topic
- error analysis
- Subject
- Topic
- superconvergence,fully discretized,points per wavelength,WENO limiter
- Subject (FAST)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/915028")
- Topic
- Error analysis (Mathematics)
- Record Information
- Record Content Source (marcorg)
- RPB
- Record Creation Date
(encoding="iso8601")
- 20121023
- Language
- Language Term:
Code (ISO639-2B)
- eng
- Language Term:
Text
- English
- Abstract
- This dissertation presents wave resolution properties and weighted essentially non-oscillatory limiter for discontinuous Galerkin methods solving hyperbolic conservation laws. <br/>
<br/>
In this dissertation, using Fourier analysis, we provide a quantitative error analysis for the semi-discrete DG method applied to time dependent linear convection equations with periodic boundary conditions. We apply the same technique to show that the error is of order $k+2$ superconvergent at Radau points on each element and of order $2k+1$ superconvergent at the downwind point of each element, when using piecewise polynomials of degree $k$. An analysis of the fully discretized approximation is also provided. We compute the number of points per wavelength required to obtain a fixed error <br/>
for several fully discrete schemes. <br/>
<br/>
We also investigate a simple limiter using<br/>
weighted essentially non-oscillatory (WENO) methodology for the Runge-Kutta discontinuous Galerkin (RKDG) methods solving conservation laws, with the goal of obtaining a robust<br/>
and high order limiting procedure to simultaneously achieve uniform high order accuracy and sharp, non-oscillatory shock transitions. The idea of this limiter is to reconstruct the entire polynomial, instead of reconstructing point values or moments in <br/>
the classical WENO reconstructions. That is, the reconstruction polynomial on the target cell is a convex combination of polynomials on this cell and its neighboring cells and the nonlinear weights of the convex combination follow the <br/>
classical WENO procedure. The main advantage of this limiter is its simplicity in implementation, especially for multi-dimensional meshes.<br/>
<br/>
- Identifier:
DOI
- 10.7301/Z0ZW1J6D
- Access Condition:
rights statement
(href="http://rightsstatements.org/vocab/InC/1.0/")
- In Copyright
- Access Condition:
restriction on access
- Collection is open for research.
- Type of Resource (primo)
- dissertations