Results 71 to 80 of about 37,916 (260)
Quarterly Journal of the Royal Meteorological Society, EarlyView.We present a compatible finite‐element discretisation of a general formulation of moist shallow‐water equations, with the aim of providing a simple model to advance understanding of physics–dynamics coupling. We detail set‐ups and show three moist shallow‐water test cases in four different model formulations. The results demonstrate differences between
Nell Hartney +2 more
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Penalty‐free discontinuous Galerkin method
International Journal for Numerical Methods in EngineeringAbstractIn this article, we present a new high‐order discontinuous Galerkin (DG) method, in which neither a penalty parameter nor a stabilization parameter is needed. We refer to this method as penalty‐free DG. In this method, the trial and test functions belong to the broken Sobolev space, in which the functions are in general discontinuous on the ...
Jan Jaśkowiec, N. Sukumar
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The Discontinuous Galerkin Method with Diffusion [PDF]
Mathematics of Computation, 1992 Let \(\Omega\subset \mathbb{R}^ 2\) be a bounded polygon and \(\alpha=(\alpha_ 1,\alpha_ 2)\) a unit vector. The author considers the following class of constant-coefficient convection-diffusion equations: (1) \(u_ \alpha-\sigma_ 1u_{xx}-\sigma_ 2u_{yy}=f\), where \((x,y)\in \Omega\), \(u_ \alpha=\alpha\cdot\bigtriangledown u\) and \(\sigma_ 1\) and \(\
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Embedded Trefftz discontinuous Galerkin methods
International Journal for Numerical Methods in Engineering, 2023 AbstractIn Trefftz discontinuous Galerkin methods a partial differential equation is discretized using discontinuous shape functions that are chosen to be elementwise in the kernel of the corresponding differential operator. We propose a new variant, the embedded Trefftz discontinuous Galerkin method, which is the Galerkin projection of an underlying ...
Christoph Lehrenfeld, Paul Stocker
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Journal of Mathematics, 2017 In this paper, we investigate a mixed discontinuous Galerkin approximation of time dependent convection diffusion optimal control problem with control constraints based on the combination of a mixed finite element method for the elliptic part and a ...
Qingjin Xu, Zhaojie Zhou
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A High-Order Discontinuous Galerkin Method for Solving Preconditioned Euler Equations
Applied Sciences, 2022 A high-order discontinuous Galerkin (DG) method is presented for solving the preconditioned Euler equations with an explicit or implicit time marching scheme.
Huanqin Gao +4 more
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, 2015 In this paper we present an efficient discretization method for the solution of the unsteady incompressible Navier-Stokes equations based on a high order (Hybrid) Discontinuous Galerkin formulation.
Lehrenfeld, Christoph +1 more
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Ensemble Kalman filter in latent space using a variational autoencoder pair
Quarterly Journal of the Royal Meteorological Society, EarlyView.The use of the ensemble Kalman filter (EnKF) in strongly nonlinear or constrained atmospheric, oceanographic, or sea‐ice models can be challenging. Applying the EnKF in the latent space of a variational autoencoder (VAE) ensures that the ensemble members satisfy the balances and constraints present in the model.
Ivo Pasmans +4 more
wiley +1 more source
Convergence of adaptive discontinuous Galerkin methods
Mathematics of Computation, 2018 We develop a general convergence theory for adaptive discontinu- ous Galerkin methods for elliptic PDEs covering the popular SIPG, NIPG and LDG schemes as well as all practically relevant marking strategies. Another key feature of the presented result is, that it holds for penalty parameters only necessary for the standard analysis of the respective ...
Kreuzer, Christian +1 more
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Membrane finite element method for simulating fluid flow in porous medium
Water Science and Engineering, 2009 A new membrane finite element method for modeling fluid flow in a porous medium is presented in order to quickly and accurately simulate the geo-membrane fabric used in civil engineering.
Mei-li Zhan +4 more
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