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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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Lee, David (author), Palha da Silva Clérigo, A. (author)A new horizontally explicit/vertically implicit (HEVI) time splitting scheme for atmospheric modelling is introduced, for which the horizontal divergence terms are applied within the implicit vertical substep. The new HEVI scheme is implemented in conjunction with a mixed mimetic spectral element spatial discretisation and semiimplicit...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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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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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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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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Azijli, I. (author), Sciacchitano, A. (author), Ragni, D. (author), Palha da Silva Clérigo, A. (author), Dwight, R.P. (author)A methodology for a posteriori uncertainty quantification of pressure data retrieved from particle image velocimetry (PIV) is proposed. It relies upon the Bayesian framework, where the posterior distribution (probability distribution of the true velocity, given the PIV measurements) is obtained from the prior distribution (prior knowledge of...journal article 2016
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Azijli, I. (author), Sciacchitano, A. (author), Ragni, D. (author), Palha da Silva Clerigo, A. (author), Dwight, R.P. (author)The present work proposes a methodology for the a posteriori quantification of the uncertainty of pressure data retrieved from PIV measurements. It relies upon the Bayesian framework, where the posterior distribution (probability distribution of the true velocity, given the PIV measurements) is obtained from the prior distribution (prior...conference paper 2015