Journal Article10.1007/s10915-022-01779-x
Optimal Strong Convergence of Finite Element Methods for One-Dimensional Stochastic Elliptic Equations with Fractional Noise
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About: This article is published in Journal of Scientific Computing. The article was published on 18 Feb 2022. The article focuses on the topics: Computer science & Fractional Brownian motion.
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Citations
The role of stabilization in the virtual element method: A survey
Lorenzo Mascotto
TL;DR: The virtual element method stabilization analysis overview summarizes the main mathematical results concerning the stabilization of the method and introduces newcomers to the field. It includes summaries of proofs for two dimensional "nodal" conforming and nonconforming virtual element spaces, extensions to other virtual elements, and discussions on interpolation estimates.
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Immersed virtual element methods for electromagnetic interface problems in three dimensions
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An immersed Crouzeix–Raviart finite element method in 2D and 3D based on discrete level set functions
TL;DR: In this article , a unified framework for both 2D and 3D immersed finite element (IFE) methods is presented, where the interface is approximated via discrete level set functions and the optimal bounds for the IFE interpolation errors are proved on shape-regular triangulations.
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The virtual element method for the 3D resistive magnetohydrodynamic mode
TL;DR: In this paper , a four-field virtual element discretization for the time-dependent resistive magnetohydrodynamics equations in three space dimensions is presented, focusing on the semi-discrete formulation.
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References
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Intermittency of velocity time increments in turbulence.
Laurent Chevillard,Stéphane Roux,Emmanuel Lévêque,Nicolas Mordant,Jean-François Pinton,Alain Arneodo +5 more
TL;DR: The static case and the virtual probe cases share many properties with Eulerian velocity statistics, and the dynamic case is clearly different; it bears the signature of the global dynamics of the flow.
Semi-discretization of stochastic partial differential equations on R 1 by a finite-difference method
TL;DR: A finite-difference scheme for the approximation of partial differential equations in R 1, with additional stochastic noise, using the weighted Lp-theory of SPDE and a sup-norm error estimate is derived and the rate of convergence is given.
On spectral simulation of fractional Brownian motion
A. B. Dieker,M. Mandies +1 more
- 01 Jan 2003
TL;DR: In this paper, the authors study the class of approximate methods that are based on the spectral properties of fBm's stationary incremental process, usually called fractional Gaussian noise (fGn).
Numerical Methods for Second-Order Stochastic Differential Equations
TL;DR: Numerical experiments, comparing the implicit midpoint rule with Heun and leapfrog methods on nonlinear equations with additive or multiplicative noise, produce behavior similar to the linear case.