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Kranenburg, W.M. (author), van Keulen, Daan (author), Gerritsma, A. (author), Huismans, Y. (author)
We investigate the changes in surface water salinity intrusion lengths for estuaries around the world under influence of climate change. To do this, we make use of information from global data sets on present river geometry and present and predicted future river discharges, mean sea levels and tidal ranges, which we combine with various models...
conference paper 2023
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Zhang, Y. (author), Jain, V. (author), Palha, A. (author), Gerritsma, M.I. (author)
In this paper, we present a hybrid mimetic method which solves the mixed formulation of the Poisson problem on curvilinear quadrilateral meshes. The method is hybrid in the sense that the domain is decomposed into multiple disjoint elements and the interelement continuity is enforced using a Lagrange multiplier. The method is mimetic in the...
conference paper 2020
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Zhang, Yi (author), Jain, V. (author), Palha, A. (author), Gerritsma, M.I. (author)
In this paper, we will show that the equivalence of a div-grad Neumann problem and a grad-div Dirichlet problem can be preserved at the discrete level in 3-dimensional curvilinear domains if algebraic dual polynomial representations are employed. These representations will be introduced. Proof of the equivalence at the discrete level follows...
conference paper 2020
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Jain, V. (author), Fisser, Joël (author), Palha, A. (author), Gerritsma, M.I. (author)
We present a hybrid mimetic spectral element formulation for Darcy flow. The discrete representations for (1) conservation of mass, and (2) inter-element continuity, are topological relations that lead to sparse matrix systems. These constraints are independent of the element size and shape, and thus invariant under mesh transformations. The...
conference paper 2020
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Gerritsma, M.I. (author), Palha, A. (author)
In this paper the spectral mimetic least-squares method is applied to a two-dimensional div-curl system. A test problem is solved on orthogonal and curvilinear meshes and both h- and p-convergence results are presented. The resulting solutions will be pointwise divergence-free for these test problems. For N> 1 optimal convergence rates on...
conference paper 2018
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Bochev, P. (author), Gerritsma, M.I. (author)
We present a spectral mimetic least-squares method which is fully conservative and decouples the primal and dual variables.
conference paper 2014
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de Bruijn, Roger (author), Huijs, Fons (author), Bunnik, Tim (author), Huijsmans, Rene (author), Gerritsma, Marc (author)
conference paper 2011
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Gerritsma, M.I. (author)
conference paper 2008
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Gerritsma, M.I. (author), Vos, P. (author), Van der Steen, J.B. (author)
conference paper 2008
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Oldenziel, G. (author), Gerritsma, M.I. (author)
This paper describes the use of the Least-Squares Spectral Element Method for non-linear hyperbolic equations. The one-dimensional inviscid Burgers equation is specifically subject of investigation. A second order backward difference method is used for time stepping. The behaviour of this formulation is examined by application to a testcase...
conference paper 2006
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Vos, P.E.J. (author), Gerritsma, M.I. (author)
This papers describes the use of the Least-Squares Spectral Element Method to polynomial Chaos to solve stochastic partial differential equations. The method will be described in detail and a comparison will be presented between the least-squares projection and the conventional Galerkin projection.
conference paper 2006
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Van Dalen, W.R. (author), Gerritsma, M.I. (author)
This paper discusses the use of the Least-Squares Spectral Element Method in solving the linear, 1-dimensional advection-reaction equation. Well-posedness of the Least-Squares formulation will be derived. The formulation and its results will be compared to the standard Galerkin Spectral Element Method.
conference paper 2006
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Van Dalen, W.R. (author), Gerritsma, M.I. (author)
This paper discusses the use of the Least-Squares Spectral Element Method in solving the linear, 1-dimensional advection-reaction equation. Well-posedness of the Least-Squares formulation will be derived. The formulation and its results will be compared to the standard Galerkin Spectral Element Method.
conference paper 2006
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Vos, P.E.J. (author), Gerritsma, M.I. (author)
This papers describes the use of the Least-Squares Spectral Element Method to polynomial Chaos to solve stochastic partial differential equations. The method will be described in detail and a comparison will be presented between the least-squares projection and the conventional Galerkin projection.
conference paper 2006
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Oldenziel, G. (author), Gerritsma, M.I. (author)
This paper describes the use of the Least-Squares Spectral Element Method for non-linear hyperbolic equations. The one-dimensional inviscid Burgers equation is specifically subject of investigation. A second order backward difference method is used for time stepping. The behaviour of this formulation is examined by application to a testcase...
conference paper 2006
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Cnossen, J.M. (author), Bijl, H. (author), Gerritsma, M.I. (author), Koren, B. (author)
For goal-oriented model adaptation a model-error estimator is required to drive the adaptation process. In recent years publications have appeared on the dual-weighted residual (DWR) method in the application of model-error estimation in output functionals. In this paper we study the application of the DWR method for convection-diffusion...
conference paper 2006
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De Maerschalck, B. (author), Gerritsma, M.I. (author)
Least-squares methods for partial differential equations are based on a norm-equivalence between the error norm and the residual norm. The resulting algebraic system of equations, which is symmetric positive definite, can also be obtained by solving a weighted collocation scheme using least-squares to solve the resulting algebraic equations....
conference paper 2006
document
De Maerschalck, B. (author), Gerritsma, M.I. (author)
Least-squares methods for partial differential equations are based on a norm-equivalence between the error norm and the residual norm. The resulting algebraic system of equations, which is symmetric positive definite, can also be obtained by solving a weighted collocation scheme using least-squares to solve the resulting algebraic equations....
conference paper 2006
document
Cnossen, J.M. (author), Bijl, H. (author), Gerritsma, M.I. (author), Koren, B. (author)
For goal-oriented model adaptation a model-error estimator is required to drive the adaptation process. In recent years publications have appeared on the dual-weighted residual (DWR) method in the application of model-error estimation in output functionals. In this paper we study the application of the DWR method for convection-diffusion...
conference paper 2006
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Kwakkel, M. (author), Gerritsma, M.I. (author)
In this work a new approach to time dependent problems in combination with the Least-Squares Spectral Element Method (LSQSEM) will be discussed. Various timestepping formulations will be presented. These time-stepping formulations will be compared to the full space-time formulation. It will be shown that time-stepping formulations give accurate...
conference paper 2006
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