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document
Vuik, M.J. (author)
This dissertation addresses practical use of multiwavelets and outlier detection for troubled-cell 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: non-physical...
doctoral thesis 2017
document
Vuik, M.J. (author), Ryan, J.K. (author)
In Vuik and Ryan [J. Comput. Phys., 270 (2014), pp. 138--160] we studied the use of troubled-cell indicators for discontinuity detection in nonlinear hyperbolic partial differential equations and introduced a new multiwavelet technique to detect troubled cells. We found that these methods perform well as long as a suitable, problem-dependent...
journal article 2016
document
Van Slingerland, P. (author), Ryan, J.K. (author), Vuik, C. (author)
Position-dependent smoothness-increasing accuracy-conserving (SIAC) filtering is a promising technique not only in improving the order of the numerical solution obtained by a discontinuous Galerkin (DG) method but also in increasing the smoothness of the field and improving the magnitude of the errors. This was initially established as an...
journal article 2011