Analysis of Compatible Discrete Operator Schemes for the Stokes Equations on Polyhedral Meshes [PDF]
, 2014 Compatible Discrete Operator schemes preserve basic properties of the continuous model at the discrete level. They combine discrete differential operators that discretize exactly topological laws and discrete Hodge operators that approximate constitutive
Bonelle, Jerome, Ern, Alexandre
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Addressing Integration Error for Polygonal Finite Elements Through Polynomial Projections: A Patch Test Connection [PDF]
, 2013 Polygonal finite elements generally do not pass the patch test as a result of quadrature error in the evaluation of weak form integrals. In this work, we examine the consequences of lack of polynomial consistency and show that it can lead to a ...
Paulino, Glaucio H., Talischi, Cameron
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Mimetic finite difference operators and higher order quadratures
GEM - International Journal on Geomathematics, 2023 AbstractMimetic finite difference operators $$\textbf{D}$$ D , $$\textbf{G}$$ G are discrete analogs of the continuous divergence (div) and gradient (grad) operators. In the discrete sense, these discrete operators satisfy the same properties as those of their continuum counterparts ...
Anand Srinivasan +4 more
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Oil & Gas Science and Technology, 2017 Nowadays, some frameworks like Arcane and Dune offer a number of advanced tools to deal with the complexity related to parallelism, meshes and linear solvers.
Gratien Jean-Marc
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The curved mimetic finite difference method: Allowing grids with curved faces
Journal of Computational Physics, 2023 We present a new mimetic finite difference method for diffusion problems that converges on grids with \textit{curved} (i.e., non-planar) faces. Crucially, it gives a symmetric discrete problem that uses only one discrete unknown per curved face. The principle at the core of our construction is to abandon the standard definition of local consistency of ...
Pitassi S. +4 more
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Numerical analysis for the pure Neumann control problem using the gradient discretisation method
, 2017 The article discusses the gradient discretisation method (GDM) for distributed optimal control problems governed by diffusion equation with pure Neumann boundary condition. Using the GDM framework enables to develop an analysis that directly applies to a
Droniou, Jerome +2 more
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The Mimetic Methods Toolkit: An object-oriented API for Mimetic Finite Differences
Journal of Computational and Applied Mathematics, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Eduardo J. Sanchez +2 more
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Exact computation of the Maximum Entropy Potential of spiking neural networks models [PDF]
, 2014 Understanding how stimuli and synaptic connectivity in uence the statistics of spike patterns in neural networks is a central question in computational neuroscience.
Cessac, Bruno, Cofre, Rodrigo
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The mimetic finite difference method for the Landau–Lifshitz equation [PDF]
Journal of Computational Physics, 2017 The Landau-Lifshitz equation describes the dynamics of the magnetization inside ferromagnetic materials. This equation is highly nonlinear and has a non-convex constraint (the magnitude of the magnetization is constant) which pose interesting challenges in developing numerical methods.
Kim, Eugenia, Lipnikov, Konstantin
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On the Virtual Element Method for Topology Optimization on polygonal meshes: a numerical study [PDF]
, 2016 It is well known that the solution of topology optimization problems may be affected both by the geometric properties of the computational mesh, which can steer the minimization process towards local (and non-physical) minima, and by the accuracy of the ...
Antonietti, Paola F. +3 more
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