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Li, Xiaozhou (author), Ryan, J.K. (author), Kirby, Robert M. (author), Vuik, Cornelis (author)Smoothness-increasing accuracy-conserving (SIAC) filtering is an area of increasing interest because it can extract the “hidden accuracy” in discontinuous Galerkin (DG) solutions. It has been shown that by applying a SIAC filter to a DG solution, the accuracy order of the DG solution improves from order k+ 1 to order 2 k+ 1 for linear...journal article 2019
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Geevers, S. (author), Mulder, W.A. (author), van der Vegt, J. J.W. (author)We analyse the dispersion properties of two types of explicit finite element methods for modelling acoustic and elastic wave propagation on tetrahedral meshes, namely mass-lumped finite element methods and symmetric interior penalty discontinuous Galerkin methods, both combined with a suitable Lax–Wendroff time integration scheme. The...journal article 2018
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van Zwieten, J.S.B. (author), Sanderse, B. (author), Hendrix, M.H.W. (author), Vuik, Cornelis (author), Henkes, R.A.W.M. (author)One-dimensional models for multiphase flow in pipelines are commonly discretised using first-order Finite Volume (FV) schemes, often combined with implicit time-integration methods. While robust, these methods introduce much numerical diffusion depending on the number of grid points. In this paper we propose a high-order, space-time...journal article 2017
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Li, X. (author)In this dissertation, we focus on exploiting superconvergence for discontinuous Galerkin methods and constructing a superconvergence extraction technique, in particular, Smoothness-Increasing Accuracy-Conserving (SIAC) filtering. The SIAC filtering technique is based on the superconvergence property of discontinuous Galerkin methods and aims to...doctoral thesis 2015