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Multiscale Hybrid-Mixed Method
SIAM Journal on Numerical Analysis, 2013 This work presents a priori and a posteriori error analyses of a new multiscale hybrid-mixed method (MHM) for an elliptic model. Specially designed to incorporate multiple scales into the construction of basis functions, this finite element method relaxes the continuity of the primal variable through the action of Lagrange multipliers, while assuring ...
Rodolfo Araya +2 more
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Oversampling for the Multiscale Finite Element Method [PDF]
Multiscale Modeling and Simulation, 2013 This paper reviews standard oversampling strategies as performed in the Multiscale Finite Element Method (MsFEM). Common to those approaches is that the oversampling is performed in the full space restricted to a patch but including coarse finite element functions.
Daniel Peterseim, Patrick Henning
exaly +4 more sources
Convergence of a Discontinuous Galerkin Multiscale Method [PDF]
SIAM Journal on Numerical Analysis, 2013 A convergence result for a discontinuous Galerkin multiscale method for a second order elliptic problem is presented. We consider a heterogeneous and highly varying diffusion coefficient in $L^\infty(Ω,\mathbb{R}^{d\times d}_{sym})$ with uniform spectral bounds and without any assumption on scale separation or periodicity.
Daniel Peterseim +2 more
exaly +4 more sources
Baroclinic Instability of a Time-Dependent Zonal Shear Flow
Atmosphere, 2022 In the real atmosphere, the development of large-scale motion is often related to the baroclinic properties of the atmosphere. So, it is necessary to discuss the stability condition of baroclinic flow. It is advantageous to use a layered model to discuss
Chengzhen Guo, Jian Song
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Contrast-Independent Partially Explicit Time Discretizations for Quasi Gas Dynamics
Mathematics, 2022 In the paper, we study a design and stability of contrast-independent partially explicit time discretizations for Quasi-Gas-Dynamics (QGD) Equations in multiscale high-contrast media.
Boris Chetverushkin +2 more
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Contrast-Independent, Partially-Explicit Time Discretizations for Nonlinear Multiscale Problems
Mathematics, 2021 This work continues a line of work on developing partially explicit methods for multiscale problems. In our previous works, we considered linear multiscale problems where the spatial heterogeneities are at the subgrid level and are not resolved. In these
Eric T. Chung +3 more
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GKS and UGKS for High-Speed Flows
Aerospace, 2021 The gas-kinetic scheme (GKS) and the unified gas-kinetic scheme (UGKS) are numerical methods based on the gas-kinetic theory, which have been widely used in the numerical simulations of high-speed and non-equilibrium flows.
Yajun Zhu, Chengwen Zhong, Kun Xu
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The heterogeneous multiscale method [PDF]
Acta Numerica, 2012 The heterogeneous multiscale method (HMM), a general framework for designing multiscale algorithms, is reviewed. Emphasis is given to the error analysis that comes naturally with the framework. Examples of finite element and finite difference HMM are presented.
Assyr Abdulle +3 more
openaire +1 more source
Multiscale approach of the equivalent thermal conductivity of modified foam-filled and non-filled ho
Journal of Thermal Engineering, 2021 The energy loss through building components resulting in higher energy consumption, thus energy saving has become an essential aspect in design and comfort.
Atheer HASHİM +4 more
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Fluids, 2021 In this paper, we consider the poroelasticity problem in fractured and heterogeneous media. The mathematical model contains a coupled system of equations for fluid pressures and displacements in heterogeneous media.
Aleksei Tyrylgin +4 more
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