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Adaptive generalized multiscale approximation of a mixed finite element method with velocity elimination
[article]
2020
arXiv
pre-print
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In this paper, we propose offline and online adaptive enrichment algorithms for the generalized multiscale approximation of a mixed finite element method with velocity elimination to solve the subsurface ...
A series of numerical examples are provided to highlight the performance of both these two adaptive methods and also validate the theoretical analysis. ...
Recently, a generalized multiscale approximation of a mixed finite element method (MFEM) with velocity elimination has been developed in [27] for the subsurface flow problem, which also follows the GMsFEM ...
arXiv:2007.08934v1
fatcat:kfilpurzyvfszn53c4yntmob3u
Generalized multiscale approximation of a multipoint flux mixed finite element method for Darcy-Forchheimer model
[article]
2020
arXiv
pre-print
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The problem is solved in the framework of generalized multiscale finite element methods (GMsFEM) combined with a multipoint flux mixed finite element (MFMFE) method. appropriate mixed finite element spaces ...
We consider the MFMFE method that utilizes the lowest order Brezzi-Douglas-Marini (BDM_1) mixed finite element spaces for the velocity and pressure approximation. ...
[13] utilized the mixed generalized multiscale finite element method (mixed GMsFEM) to approximate the Darcy-Forchheimer model on the coarse grid. ...
arXiv:2007.08942v1
fatcat:opanrqhir5cn3l23vtautmokg4
Multiscale Methods for Model Order Reduction of Non Linear Multiphase Flow Problems
[article]
2018
arXiv
pre-print
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An expanded mixed finite element formulation is used to separate the spatial scales between non-linear, flow and transport problems. ...
We attempt to present a comparison between two such model order reduction techniques, namely: (1) adaptive numerical homogenization and (2) generalized multiscale basis functions. ...
Generalized mixed multiscale method In this subsection, we will present a numerical result of the generalized mixed multiscale method for black oil equation. ...
arXiv:1803.03721v1
fatcat:z2xtzt7xx5caxepbzpb6g2xywm
A comparison of multiscale methods for elliptic problems in porous media flow
2008
Computational Geosciences
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We review and perform comparison studies for three recent multiscale methods for solving elliptic problems in porous media flow; the multiscale mixed finite-element method, the numerical subgrid upscaling ...
We therefore choose to also compare the multiscale methods with a state-of-theart upscaling method-the adaptive local-global upscaling method, which may be viewed as a multiscale method when coupled with ...
We are also grateful to the reviewers of this paper for numerous helpful comments and suggestions. ...
doi:10.1007/s10596-007-9074-6
fatcat:yseiamirmzcn7fcipv57r4bhea
Implementation of a mortar mixed finite element method using a Multiscale Flux Basis
2009
Computer Methods in Applied Mechanics and Engineering
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This paper provides a new implementation of a multiscale mortar mixed finite element method for second order elliptic problems. ...
The gain in computational efficiency increases with the number of subdomains. ...
Our choice of mixed finite element method for the discretization is motivated by its local elementwise conservation of mass and accurate velocity approximation. ...
doi:10.1016/j.cma.2009.09.009
fatcat:miyz4c2tufe57g2tugnd4ooaku
Multiscale Simulations for Coupled Flow and Transport Using the Generalized Multiscale Finite Element Method
2015
Computation
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We construct a coarse grid solver based on the Generalized Multiscale Finite Element Method (GMsFEM) for a coupled system. ...
Our numerical results show that with only a few basis functions per coarse block, we can achieve a good approximation. ...
equations within the context of Generalized Multiscale Finite Element Method (GMsFEM). ...
doi:10.3390/computation3040670
fatcat:ljm5o3wgdrf5bhejpfayka7x34
Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods
2016
Journal of Computational Physics
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We present a general adaptive multiscale model reduction framework, the Generalized Multiscale Finite Element Method. ...
In this paper, we discuss a general multiscale model reduction framework based on multiscale finite element methods. We give a brief overview of related multiscale methods. ...
The proposed methods take their origin in Multiscale Finite Element Methods [50, 54] and Generalized Finite Element Methods [60] . ...
doi:10.1016/j.jcp.2016.04.054
fatcat:b3xi4jz5ezhlvpvtqkd5wnhwx4
A Multiscale Method for Modeling Transport in Porous Media on Unstructured Corner-Point Grids
2008
Journal of Algorithms & Computational Technology
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In this method the global flow is computed on a coarse grid scale, but information from a fine scale velocity field is used to improve accuracy. ...
In this paper we propose a multiscale method for solving transport equations on a coarse grid. ...
The elliptic part is solved on a coarse grid with a multiscale mixed finite element method [5, 3] . This method provides high resolution velocity fields at low computational cost. ...
doi:10.1260/174830108784646616
fatcat:3wyaogepkfhgbkiioqnk76t34e
A hybrid HDMR for mixed multiscale finite element method with application for flows in random porous media
[article]
2013
arXiv
pre-print
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To treat the heterogeneity, we use a mixed multiscale finite element method (MMsFEM) to simulate each of derived stochastic models. ...
This significantly enhances the accuracy of the multiscale simulation. ...
Mixed multiscale finite element method. ...
arXiv:1211.6510v2
fatcat:qlahhxu3hjggncjbiwqelod7iq
Multiscale Computations for Flow and Transport in Porous Media
[chapter]
2009
Series in Contemporary Applied Mathematics
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This paper reviews some of the recent advances in developing systematic multiscale methods with particular emphasis on multiscale finite element methods with applications to flow and transport in heterogeneous ...
This manuscript is not intended to be a general survey paper on this topic. The discussion is limited by the scope of the lectures and expertise of the author. ...
Mixed finite element methods with limited global information One can carry out the analysis of mixed multiscale finite element method with limited global information. ...
doi:10.1142/9789814273268_0003
fatcat:c2otu3os5vd43neqiopwbpfkqy
Locally conservative, stabilized finite element methods for variably saturated flow
2008
Computer Methods in Applied Mechanics and Engineering
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Here, we consider conforming finite element discretizations based on a multiscale formulation along with recently developed, local postprocessing schemes. ...
The resulting approach maintains the basic flexibility and appeal of traditional finite element methods, while controlling nonphysical oscillations and producing element-wise massconservative velocity ...
As a point of reference, we also considered a locally conservative nonconforming finite element approximation that coincides with a mixed hybrid finite element approximations in many cases. ...
doi:10.1016/j.cma.2008.06.005
fatcat:r2p7kyyz3zg4zpnpq3cqu6kdta
Multiscale Computations for Flow and Transport in Heterogeneous Media
[chapter]
2008
Lecture notes in mathematics
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Extra effort is made in developing a multiscale computational method that can be potentially used for practical multiscale for problems with a large range of nonseparable scales. ...
This homogenization theory provides the critical guideline for designing effective multiscale methods. In part 2, I will review some recent developments of multiscale finite element (volume) methods. ...
Mixed finite element methods with limited global information One can carry out the analysis of mixed multiscale finite element method with limited global information. ...
doi:10.1007/978-3-540-79574-2_4
fatcat:wcihalffjvfobppsdjxjrlywva
Expanded Mixed Multiscale Finite Element Methods and Their Applications for Flows in Porous Media
2012
Multiscale Modeling & simulation
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We develop a family of expanded mixed Multiscale Finite Element Methods (MsFEMs) and their hybridizations for second-order elliptic equations. ...
This formulation expands the standard mixed Multiscale Finite Element formulation in the sense that four unknowns (hybrid formulation) are solved simultaneously: pressure, gradient of pressure, velocity ...
Chen and Hou developed a local multiscale basis equation for velocity and combined it with a mixed finite element formulation to propose a mixed MsFEM [14] . ...
doi:10.1137/11083143x
fatcat:y4na4xuipvf2rhzuin563nvmba
A multiscale multilevel mimetic (M3) method for well-driven flows in porous media
2010
Procedia Computer Science
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The multiscale multilevel mimetic (M 3 ) method was designed in [13] for the accurate modeling of two-phase flows in highly heterogeneous porous media on general polygonal meshes. ...
A similar elimination procedure is often used in mixed-hybrid finite element methods. ...
The multiscale multilevel mimetic (M 3 ) method [13] uses the synergy of two ideas: exact algebraic coarsening [10] and approximate (but accurate) flux coarsening, to generate a multilevel hierarchy ...
doi:10.1016/j.procs.2010.04.083
fatcat:jbseksm44rehtfkragksduuyha
Page 5004 of Mathematical Reviews Vol. , Issue 2001G
[page]
2001
Mathematical Reviews
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Basic problems of adaptation of finite-element approximations in solving multi-dimensional problems of mathematical physics are discussed. ...
The velocity block can be approximated by a domain decomposition method, e.g., of wire basket type, which is constructed from a local solver for each face of the elements, and a coarse solver related to ...
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