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Jain, V. (author), Palha da Silva Clérigo, A. (author), Gerritsma, M.I. (author)In this work we use algebraic dual spaces with a domain decomposition method to solve the Darcy equations. We define the broken Sobolev spaces and their finite dimensional counterparts. A global trace space is defined that connects the solution between the broken spaces. Use of algebraic dual spaces results in a sparse, metricfree...journal article 2023
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Zhang, Y. (author), Palha da Silva Clérigo, A. (author), Gerritsma, M.I. (author), Rebholz, Leo G. (author)We introduce a mimetic dualfield discretization which conserves mass, kinetic energy and helicity for threedimensional incompressible NavierStokes equations. The discretization makes use of a conservative dualfield mixed weak formulation where two evolution equations of velocity are employed and dual representations of the solution are...journal article 2022
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Tosti Balducci, G.B.L. (author), Chen, B. Y. (author), Möller, M. (author), Gerritsma, M.I. (author), De Breuker, R. (author)Structural mechanics is commonly modeled by (systems of) partial differential equations (PDEs). Except for very simple cases where analytical solutions exist, the use of numerical methods is required to find approximate solutions. However, for many problems of practical interest, the computational cost of classical numerical solvers running on...review 2022
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Zhang, Y. (author), Fisser, Joël (author), Gerritsma, M.I. (author)We introduce a domain decomposition structurepreserving method based on a hybrid mimetic spectral element method for threedimensional linear elasticity problems in curvilinear conforming structured meshes. The method is an equilibrium method which satisfies pointwise equilibrium of forces. The domain decomposition is established through...journal article 2021
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Zhang, Y. (author), Jain, V. (author), Palha da Silva Clérigo, 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 da Silva Clérigo, A. (author), Gerritsma, M.I. (author)In this paper, we will show that the equivalence of a divgrad Neumann problem and a graddiv Dirichlet problem can be preserved at the discrete level in 3dimensional 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 da Silva Clérigo, 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) interelement 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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Jain, V. (author), Zhang, Y. (author), Palha da Silva Clérigo, A. (author), Gerritsma, M.I. (author)Given a sequence of finite element spaces which form a de Rham sequence, we will construct dual representations of these spaces with associated differential operators which connect these spaces such that they also form a de Rham sequence. The dual representations also need to satisfy the de Rham sequence on the domain boundary. The matrix...journal article 2020
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Khan, Arbaz (author), Upadhyay, Chandra Shekhar (author), Gerritsma, M.I. (author)In this paper, an h∕p spectral element method with leastsquare formulation for parabolic interface problem will be presented. The regularity result of the parabolic interface problem is proven for nonhomogeneous interface data. The differentiability estimates and the main stability estimate theorem, using nonconforming spectral element...journal article 2018
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Gerritsma, M.I. (author), Palha da Silva Clérigo, A. (author)In this paper the spectral mimetic leastsquares method is applied to a twodimensional divcurl system. A test problem is solved on orthogonal and curvilinear meshes and both h and pconvergence results are presented. The resulting solutions will be pointwise divergencefree 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 leastsquares method which is fully conservative and decouples the primal and dual variables.conference paper 2014
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 Gerritsma, M.I. (author) lecture notes 2012
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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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De Maerschalck, B. (author), Gerritsma, M.I. (author)Leastsquares methods for partial differential equations are based on a normequivalence 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 leastsquares to solve the resulting algebraic equations....conference paper 2006
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Oldenziel, G. (author), Gerritsma, M.I. (author)This paper describes the use of the LeastSquares Spectral Element Method for nonlinear hyperbolic equations. The onedimensional 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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De Maerschalck, B. (author), Gerritsma, M.I. (author)Leastsquares methods for partial differential equations are based on a normequivalence 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 leastsquares to solve the resulting algebraic equations....conference paper 2006
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Vos, P.E.J. (author), Gerritsma, M.I. (author)This papers describes the use of the LeastSquares 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 leastsquares projection and the conventional Galerkin projection.conference paper 2006
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Cnossen, J.M. (author), Bijl, H. (author), Gerritsma, M.I. (author), Koren, B. (author)For goaloriented model adaptation a modelerror estimator is required to drive the adaptation process. In recent years publications have appeared on the dualweighted residual (DWR) method in the application of modelerror estimation in output functionals. In this paper we study the application of the DWR method for convectiondiffusion...conference paper 2006
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Van Dalen, W.R. (author), Gerritsma, M.I. (author)This paper discusses the use of the LeastSquares Spectral Element Method in solving the linear, 1dimensional advectionreaction equation. Wellposedness of the LeastSquares 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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