Abstract
This dissertation addresses practical use of multiwavelets and outlier detection for troubledcell indication for discontinuous Galerkin (DG) methods. For smooth solutions, the DG approximation converges to the exact solution with a high order of accuracy. However, problems may arise when shock waves or discontinuities appear: nonphysical spurious oscillations are formed close to these discontinuous regions. These oscillations can be prevented by applying a limiter near these regions. One of the difficulties in using a limiter is identifying the difference between a true discontinuity and a local extremum of the approximation. Troubledcell indicators can help to detect this difference and identify the discontinuous regions (socalled ’troubled cells’) where a limiter should be applied.
In this dissertation, a multiwavelet formulation is used to decompose the DG approximation. The multiwavelet coefficients act as a troubledcell indicator since they suddenly increase in the neighborhood of a discontinuity. This leads to the definition of a new multiwavelet indicator that detects elements as troubled if the coefficient is large enough in absolute value. Here, a problemdependent parameter is needed to define the strictness of the indicator. To forgo the reliance on a parameter, a new outlierdetection algorithm is defined that uses boxplot theory. This method can also be applied to different troubledcell indicators.
Results are shown for regular onedimensional and tensorproduct twodimensional meshes, as well as for irregular meshes in one dimension and triangular meshes in two dimensions.
In this dissertation, a multiwavelet formulation is used to decompose the DG approximation. The multiwavelet coefficients act as a troubledcell indicator since they suddenly increase in the neighborhood of a discontinuity. This leads to the definition of a new multiwavelet indicator that detects elements as troubled if the coefficient is large enough in absolute value. Here, a problemdependent parameter is needed to define the strictness of the indicator. To forgo the reliance on a parameter, a new outlierdetection algorithm is defined that uses boxplot theory. This method can also be applied to different troubledcell indicators.
Results are shown for regular onedimensional and tensorproduct twodimensional meshes, as well as for irregular meshes in one dimension and triangular meshes in two dimensions.
Original language  English 

Qualification  Doctor of Philosophy 
Supervisors/Advisors 

Award date  24 Jan 2017 
Print ISBNs  9789492516244 
DOIs  
Publication status  Published  2017 
Keywords
 RungeKutta discontinuous Galerkin method
 highorder methods
 limiters
 shock detection
 multiresolution analysis
 wavelets
 multiwavelets
 troubled cells
 outlier detection
 boxplots