Searched for: subject%3A%22Galerkin%255C+method%22
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Kaaks, B.J. (author), Rohde, M. (author), Kloosterman, J.L. (author), Lathouwers, D. (author)
We present a discontinuous Galerkin method for melting/solidification problems based on the “linearized enthalpy approach,” which is derived from the conservative form of the energy transport equation and does not depend on the use of a so-called mushy zone. We use the symmetric interior penalty method and the Lax–Friedrichs flux to...
journal article 2023
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Tsetas, A. (author), Tsouvalas, A. (author), Metrikine, A. (author)
The Alternating Frequency-Time (AFT) Harmonic Balance method has been widely applied in the analysis of non-linear mechanical systems under periodic excitation. Customarily, a periodic displacement is considered as ansatz in a harmonic balance analysis. In the present work, a deviation from the latter ansatz is realized and the periodicity is...
conference paper 2022
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Ex, Titus (author)
The finite element method (FEM) is a numerical method that is used to approximate the solutions to partial differential equations when solutions in the classical sense do not exist or are very hard to find. The method is used to solve problems that are relevant for industries like the automotive industry, the petroleum industry, and the aviation...
master thesis 2021
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Kadeethum, T. (author), Lee, S. (author), Ballarin, F. (author), Choo, J. (author), Nick, H.M. (author)
This paper presents a mixed finite element framework for coupled hydro-mechanical–chemical processes in heterogeneous porous media. The framework combines two types of locally conservative discretization schemes: (1) an enriched Galerkin method for reactive flow, and (2) a three-field mixed finite element method for coupled fluid flow and...
journal article 2021
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Tsetas, A. (author), Tsouvalas, A. (author), Metrikine, A. (author)
During the last decade the offshore wind industry grew ceaselessly and engineering challenges continuously arose in that area. Installation of foundation piles, known as monopiles, is one of the most critical phases in the construction of offshore wind farms. Prior to installation a drivability study is performed, by means of pile driving...
journal article 2021
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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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Stoter, Stein K.F. (author), Turteltaub, S.R. (author), Hulshoff, S.J. (author), Schillinger, Dominik (author)
We initiate the study of the discontinuous Galerkin residual-based variational multiscale (DG-RVMS) method for incorporating subgrid-scale behavior into the finite element solution of hyperbolic problems. We use the one-dimensional viscous Burgers equation as a model problem, as its energy dissipation mechanism is analogous to that of turbulent...
journal article 2018
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Stoter, Stein K.F. (author), Turteltaub, S.R. (author), Hulshoff, S.J. (author), Schillinger, Dominik (author)
We develop the general form of the variational multiscale method in a discontinuous Galerkin framework. Our method is based on the decomposition of the true solution into discontinuous coarse-scale and discontinuous fine-scale parts. The obtained coarse-scale weak formulation includes two types of fine-scale contributions. The first type...
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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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
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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
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Tol, H.J. (author), de Visser, C.C. (author), Kotsonis, M. (author)
A new methodology is presented for model reduction of linear parabolic partial differential equations (PDEs) on general geometries using multivariate splines on triangulations. State-space descriptions are derived that can be used for control design. This method uses Galerkin projection with B-splines to derive a finite set of ordinary...
journal article 2016
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Koolstra, K. (author)
Modeling electromagnetic fields in MRI involves two main challenges: the solution of the scattering problem resulting from Maxwell's equations has to be accurate and it has to be obtained within short computation time. In this thesis a method that meets both requirements is searched for. The method of moments with rooftop basis functions is used...
master thesis 2015
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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
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Ye, B. (author)
This project focuses on extending the existing model for two-dimensional laminar boundary layers to turbulent boundary layers and more importantly to include the modeling of transition to turbulence in unsteady boundary layers. The existing models are extended and a new transition model for unsteady boundary layers is developed. Successful...
master thesis 2015
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Ølgaard, K.B. (author)
In engineering, physical phenomena are often described mathematically by partial differential equations (PDEs), and a commonly used method to solve these equations is the finite element method (FEM). Implementing a solver based on this method for a given PDE in a computer program written in source code can be tedious, time consuming and error...
doctoral thesis 2013
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Koeze, D.J. (author)
In this work we examined the discretised form of Boltzmann-like transport, i.e. the neutron trans- port equation and the Boltzmann-Fokker-Plank (BFP) equation with the discontinuous Galerkin method and polynomial basis functions. In particular we examined an adaptive algorithm, which bases its decision of where to refine on the adjoint problem,...
master thesis 2012
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Ji, L. (author), Xu, Y. (author)
In (Xu and Shu in J. Sci. Comput. 40:375–390, 2009), a local discontinuous Galerkin (LDG) method for the surface diffusion of graphs was developed and a rigorous proof for its energy stability was given. Numerical simulation results showed the optimal order of accuracy. In this subsequent paper, we concentrate on analyzing a priori error...
journal article 2011
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Özdemir, H. (author), Van den Boogaard, E.F. (author)
In this study the two-dimensional, unsteady integral boundary layer equations are solved numerically together with a closure set for laminar and turbulent flows. A high-order discontinuous Galerkin method is used for the spatial discretization and a multi-stage Runge-Kutta scheme is employed for the time integration. Numerical results show good...
conference paper 2011
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