Presho, Michael; Hill, Michael A conservative generalized multiscale finite volume/element method for modeling two-phase flow with capillary pressure. (English) Zbl 1448.35151 J. Comput. Appl. Math. 381, Article ID 113026, 15 p. (2021). MSC: 35J25 35K10 65N30 PDF BibTeX XML Cite \textit{M. Presho} and \textit{M. Hill}, J. Comput. Appl. Math. 381, Article ID 113026, 15 p. (2021; Zbl 1448.35151) Full Text: DOI
Delpopolo Carciopolo, Ludovica; Formaggia, Luca; Scotti, Anna; Hajibeygi, Hadi Conservative multirate multiscale simulation of multiphase flow in heterogeneous porous media. (English) Zbl 1453.76091 J. Comput. Phys. 404, Article ID 109134, 18 p. (2020). MSC: 76M12 76S05 65M55 65M08 PDF BibTeX XML Cite \textit{L. Delpopolo Carciopolo} et al., J. Comput. Phys. 404, Article ID 109134, 18 p. (2020; Zbl 1453.76091) Full Text: DOI
Rocha, Franciane F.; Sousa, Fabricio S.; Ausas, Roberto F.; Buscaglia, Gustavo C.; Pereira, Felipe Multiscale mixed methods for two-phase flows in high-contrast porous media. (English) Zbl 1435.76082 J. Comput. Phys. 409, Article ID 109316, 20 p. (2020). MSC: 76T06 65M55 76S05 PDF BibTeX XML Cite \textit{F. F. Rocha} et al., J. Comput. Phys. 409, Article ID 109316, 20 p. (2020; Zbl 1435.76082) Full Text: DOI
Babuška, Ivo; Lipton, Robert; Sinz, Paul; Stuebner, Michael Multiscale-spectral GFEM and optimal oversampling. (English) Zbl 1442.65402 Comput. Methods Appl. Mech. Eng. 364, Article ID 112960, 28 p. (2020). MSC: 65N35 65N30 PDF BibTeX XML Cite \textit{I. Babuška} et al., Comput. Methods Appl. Mech. Eng. 364, Article ID 112960, 28 p. (2020; Zbl 1442.65402) Full Text: DOI
Fu, Shubin; Chung, Eric T. A local-global multiscale mortar mixed finite element method for multiphase transport in heterogeneous media. (English) Zbl 1453.76069 J. Comput. Phys. 399, Article ID 108906, 13 p. (2019). MSC: 76M10 76S05 76T06 65N30 65N55 PDF BibTeX XML Cite \textit{S. Fu} and \textit{E. T. Chung}, J. Comput. Phys. 399, Article ID 108906, 13 p. (2019; Zbl 1453.76069) Full Text: DOI
Abreu, Eduardo; Díaz, Ciro; Galvis, Juan A convergence analysis of generalized multiscale finite element methods. (English) Zbl 1452.65319 J. Comput. Phys. 396, 303-324 (2019). MSC: 65N30 65N12 35J47 PDF BibTeX XML Cite \textit{E. Abreu} et al., J. Comput. Phys. 396, 303--324 (2019; Zbl 1452.65319) Full Text: DOI
Nguyen, Lam H.; Schillinger, Dominik The multiscale finite element method for nonlinear continuum localization problems at full fine-scale fidelity, illustrated through phase-field fracture and plasticity. (English) Zbl 1452.74110 J. Comput. Phys. 396, 129-160 (2019). MSC: 74S05 74R10 65N30 65N55 65Z05 PDF BibTeX XML Cite \textit{L. H. Nguyen} and \textit{D. Schillinger}, J. Comput. Phys. 396, 129--160 (2019; Zbl 1452.74110) Full Text: DOI
Yang, Yanfang; Fu, Shubin; Chung, Eric T. A two-grid preconditioner with an adaptive coarse space for flow simulations in highly heterogeneous media. (English) Zbl 1452.76241 J. Comput. Phys. 391, 1-13 (2019). MSC: 76S05 76M10 65M60 76T06 PDF BibTeX XML Cite \textit{Y. Yang} et al., J. Comput. Phys. 391, 1--13 (2019; Zbl 1452.76241) Full Text: DOI
Jiang, Jiamin; Tchelepi, Hamdi A. Nonlinear acceleration of sequential fully implicit (SFI) method for coupled flow and transport in porous media. (English) Zbl 1441.76080 Comput. Methods Appl. Mech. Eng. 352, 246-275 (2019). MSC: 76M12 65M08 74F10 74S10 76S05 PDF BibTeX XML Cite \textit{J. Jiang} and \textit{H. A. Tchelepi}, Comput. Methods Appl. Mech. Eng. 352, 246--275 (2019; Zbl 1441.76080) Full Text: DOI
Yang, Yanfang; Shi, Ke; Fu, Shubin Multiscale hybridizable discontinuous Galerkin method for flow simulations in highly heterogeneous media. (English) Zbl 1440.65237 J. Sci. Comput. 81, No. 3, 1712-1731 (2019). MSC: 65N30 65N35 65M06 65M08 76S05 76T06 35Q35 PDF BibTeX XML Cite \textit{Y. Yang} et al., J. Sci. Comput. 81, No. 3, 1712--1731 (2019; Zbl 1440.65237) Full Text: DOI
Liu, Yujie; Wang, Junping; Zou, Qingsong A conservative flux optimization finite element method for convection-diffusion equations. (English) Zbl 1422.65398 SIAM J. Numer. Anal. 57, No. 3, 1238-1262 (2019). MSC: 65N30 65N15 65N12 35B45 35J50 76S05 76T99 76R99 65N08 35Q35 PDF BibTeX XML Cite \textit{Y. Liu} et al., SIAM J. Numer. Anal. 57, No. 3, 1238--1262 (2019; Zbl 1422.65398) Full Text: DOI arXiv
Akbari, Hani; Engsig-Karup, Allan P.; Ginting, Victor; Pereira, Felipe A multiscale direct solver for the approximation of flows in high contrast porous media. (English) Zbl 1444.76101 J. Comput. Appl. Math. 359, 88-101 (2019). MSC: 76S05 65N55 35Q35 PDF BibTeX XML Cite \textit{H. Akbari} et al., J. Comput. Appl. Math. 359, 88--101 (2019; Zbl 1444.76101) Full Text: DOI
Nguyen, Lam H.; Schillinger, Dominik A residual-driven local iterative corrector scheme for the multiscale finite element method. (English) Zbl 1416.65460 J. Comput. Phys. 377, 60-88 (2019). MSC: 65N30 65Y05 35J15 PDF BibTeX XML Cite \textit{L. H. Nguyen} and \textit{D. Schillinger}, J. Comput. Phys. 377, 60--88 (2019; Zbl 1416.65460) Full Text: DOI
Ganapathy, Chandrashekar; Voskov, Denis Multiscale reconstruction in physics for compositional simulation. (English) Zbl 1416.76148 J. Comput. Phys. 375, 747-762 (2018). MSC: 76M12 76S05 76T10 PDF BibTeX XML Cite \textit{C. Ganapathy} and \textit{D. Voskov}, J. Comput. Phys. 375, 747--762 (2018; Zbl 1416.76148) Full Text: DOI
Lee, Sanghyun; Wheeler, Mary F. Enriched Galerkin methods for two-phase flow in porous media with capillary pressure. (English) Zbl 1415.76456 J. Comput. Phys. 367, 65-86 (2018). MSC: 76M10 76S05 65M60 76T99 PDF BibTeX XML Cite \textit{S. Lee} and \textit{M. F. Wheeler}, J. Comput. Phys. 367, 65--86 (2018; Zbl 1415.76456) Full Text: DOI
Yang, Yanfang; Chung, Eric T.; Fu, Shubin Residual driven online mortar mixed finite element methods and applications. (English) Zbl 1432.65172 J. Comput. Appl. Math. 340, 318-333 (2018). MSC: 65N30 PDF BibTeX XML Cite \textit{Y. Yang} et al., J. Comput. Appl. Math. 340, 318--333 (2018; Zbl 1432.65172) Full Text: DOI arXiv
Li, Guanglian Low-rank approximation to heterogeneous elliptic problems. (English) Zbl 1448.65238 Multiscale Model. Simul. 16, No. 1, 477-502 (2018). MSC: 65N30 65N80 31A35 35C15 35C20 PDF BibTeX XML Cite \textit{G. Li}, Multiscale Model. Simul. 16, No. 1, 477--502 (2018; Zbl 1448.65238) Full Text: DOI
Cusini, Matteo; Fryer, Barnaby; van Kruijsdijk, Cor; Hajibeygi, Hadi Algebraic dynamic multilevel method for compositional flow in heterogeneous porous media. (English) Zbl 1380.76097 J. Comput. Phys. 354, 593-612 (2018). MSC: 76M25 76S05 PDF BibTeX XML Cite \textit{M. Cusini} et al., J. Comput. Phys. 354, 593--612 (2018; Zbl 1380.76097) Full Text: DOI
Song, Fei; Deng, Weibing Multiscale discontinuous Petrov-Galerkin method for the multiscale elliptic problems. (English) Zbl 1397.65295 Numer. Methods Partial Differ. Equations 34, No. 1, 18-210 (2018). Reviewer: Konstantinos Chrysafinos (Athens) MSC: 65N30 65N15 PDF BibTeX XML Cite \textit{F. Song} and \textit{W. Deng}, Numer. Methods Partial Differ. Equations 34, No. 1, 18--210 (2018; Zbl 1397.65295) Full Text: DOI
Hwang, Feng-Nan; Su, Yi-Zhen; Yao, Chien-Chou An iteratively adaptive multiscale finite element method for elliptic interface problems. (English) Zbl 1382.65404 Appl. Numer. Math. 127, 211-225 (2018). MSC: 65N30 35J25 PDF BibTeX XML Cite \textit{F.-N. Hwang} et al., Appl. Numer. Math. 127, 211--225 (2018; Zbl 1382.65404) Full Text: DOI
Liu, Tao A wavelet multiscale method for the inverse problem of a nonlinear convection-diffusion equation. (English) Zbl 1376.65125 J. Comput. Appl. Math. 330, 165-176 (2018). MSC: 65M32 35R30 35K57 65T60 76S05 76M20 PDF BibTeX XML Cite \textit{T. Liu}, J. Comput. Appl. Math. 330, 165--176 (2018; Zbl 1376.65125) Full Text: DOI
Owhadi, Houman; Zhang, Lei Gamblets for opening the complexity-bottleneck of implicit schemes for hyperbolic and parabolic ODEs/PDEs with rough coefficients. (English) Zbl 1380.65406 J. Comput. Phys. 347, 99-128 (2017). MSC: 65N55 65T60 35R05 PDF BibTeX XML Cite \textit{H. Owhadi} and \textit{L. Zhang}, J. Comput. Phys. 347, 99--128 (2017; Zbl 1380.65406) Full Text: DOI
Hou, Thomas Y.; Hwang, Feng-Nan; Liu, Pengfei; Yao, Chien-Chou An iteratively adaptive multi-scale finite element method for elliptic PDEs with rough coefficients. (English) Zbl 1380.65268 J. Comput. Phys. 336, 375-400 (2017). MSC: 65M60 35J47 PDF BibTeX XML Cite \textit{T. Y. Hou} et al., J. Comput. Phys. 336, 375--400 (2017; Zbl 1380.65268) Full Text: DOI
Scovazzi, Guglielmo; Wheeler, Mary F.; Mikelić, Andro; Lee, Sanghyun Analytical and variational numerical methods for unstable miscible displacement flows in porous media. (English) Zbl 1375.76188 J. Comput. Phys. 335, 444-496 (2017). MSC: 76S05 76M10 65M60 76M30 76-02 PDF BibTeX XML Cite \textit{G. Scovazzi} et al., J. Comput. Phys. 335, 444--496 (2017; Zbl 1375.76188) Full Text: DOI
Daripa, Prabir; Dutta, Sourav Modeling and simulation of surfactant-polymer flooding using a new hybrid method. (English) Zbl 1380.65222 J. Comput. Phys. 335, 249-282 (2017). MSC: 65M25 65M60 35Q35 PDF BibTeX XML Cite \textit{P. Daripa} and \textit{S. Dutta}, J. Comput. Phys. 335, 249--282 (2017; Zbl 1380.65222) Full Text: DOI
Zhang, Qingfu; Huang, Zhaoqin; Yao, Jun; Wang, Yueying; Li, Yang A multiscale mixed finite element method with oversampling for modeling flow in fractured reservoirs using discrete fracture model. (English) Zbl 1383.76349 J. Comput. Appl. Math. 323, 95-110 (2017). MSC: 76M10 65M60 76S05 PDF BibTeX XML Cite \textit{Q. Zhang} et al., J. Comput. Appl. Math. 323, 95--110 (2017; Zbl 1383.76349) Full Text: DOI
Owhadi, Houman Multigrid with rough coefficients and multiresolution operator decomposition from hierarchical information games. (English) Zbl 1358.65071 SIAM Rev. 59, No. 1, 99-149 (2017). MSC: 65N55 65N75 65Y20 91A23 65T60 PDF BibTeX XML Cite \textit{H. Owhadi}, SIAM Rev. 59, No. 1, 99--149 (2017; Zbl 1358.65071) Full Text: DOI arXiv
Wu, Yuanqing; Sun, Shuyu Equivalence of two models in single-phase multicomponent flow simulations. (English) Zbl 1443.65149 Comput. Math. Appl. 71, No. 6, 1303-1316 (2016). MSC: 65M06 76S05 76T10 PDF BibTeX XML Cite \textit{Y. Wu} and \textit{S. Sun}, Comput. Math. Appl. 71, No. 6, 1303--1316 (2016; Zbl 1443.65149) Full Text: DOI
Liu, Tao A wavelet multiscale-homotopy method for the parameter identification problem of partial differential equations. (English) Zbl 1443.42024 Comput. Math. Appl. 71, No. 7, 1519-1523 (2016). MSC: 42C40 35R30 PDF BibTeX XML Cite \textit{T. Liu}, Comput. Math. Appl. 71, No. 7, 1519--1523 (2016; Zbl 1443.42024) Full Text: DOI
Liu, Tao Reconstruction of a permeability field with the wavelet multiscale-homotopy method for a nonlinear convection-diffusion equation. (English) Zbl 1410.76432 Appl. Math. Comput. 275, 432-437 (2016). MSC: 76S05 76M25 65M32 PDF BibTeX XML Cite \textit{T. Liu}, Appl. Math. Comput. 275, 432--437 (2016; Zbl 1410.76432) Full Text: DOI
Chung, Eric; Efendiev, Yalchin; Hou, Thomas Y. Adaptive multiscale model reduction with generalized multiscale finite element methods. (English) Zbl 1349.76191 J. Comput. Phys. 320, 69-95 (2016). MSC: 76M10 65N30 76S05 PDF BibTeX XML Cite \textit{E. Chung} et al., J. Comput. Phys. 320, 69--95 (2016; Zbl 1349.76191) Full Text: DOI arXiv
Song, Fei; Deng, Weibing; Wu, Haijun A combined finite element and oversampling multiscale Petrov-Galerkin method for the multiscale elliptic problems with singularities. (English) Zbl 1349.65634 J. Comput. Phys. 305, 722-743 (2016). MSC: 65N30 35B25 35J25 PDF BibTeX XML Cite \textit{F. Song} et al., J. Comput. Phys. 305, 722--743 (2016; Zbl 1349.65634) Full Text: DOI
Parramore, Elliot; Edwards, Michael G.; Pal, Mayur; Lamine, Sadok Multiscale finite-volume CVD-MPFA formulations on structured and unstructured grids. (English) Zbl 1381.76224 Multiscale Model. Simul. 14, No. 2, 559-594 (2016). MSC: 76M12 65M08 35Q35 35R05 76S05 PDF BibTeX XML Cite \textit{E. Parramore} et al., Multiscale Model. Simul. 14, No. 2, 559--594 (2016; Zbl 1381.76224) Full Text: DOI
Hou, Thomas Y.; Liu, Pengfei Optimal local multi-scale basis functions for linear elliptic equations with rough coefficients. (English) Zbl 1333.65131 Discrete Contin. Dyn. Syst. 36, No. 8, 4451-4476 (2016). MSC: 65N30 35J25 PDF BibTeX XML Cite \textit{T. Y. Hou} and \textit{P. Liu}, Discrete Contin. Dyn. Syst. 36, No. 8, 4451--4476 (2016; Zbl 1333.65131) Full Text: DOI
Jiang, Lijian; Li, Qiuqi Reduced multiscale finite element basis methods for elliptic PDEs with parameterized inputs. (English) Zbl 1382.65407 J. Comput. Appl. Math. 301, 101-120 (2016). MSC: 65N30 PDF BibTeX XML Cite \textit{L. Jiang} and \textit{Q. Li}, J. Comput. Appl. Math. 301, 101--120 (2016; Zbl 1382.65407) Full Text: DOI
Presho, Michael; Ye, S. Reduced-order multiscale modeling of nonlinear \(p\)-Laplacian flows in high-contrast media. (English) Zbl 1395.65086 Comput. Geosci. 19, No. 4, 921-932 (2015). MSC: 65M60 76S05 86-08 PDF BibTeX XML Cite \textit{M. Presho} and \textit{S. Ye}, Comput. Geosci. 19, No. 4, 921--932 (2015; Zbl 1395.65086) Full Text: DOI
Li, Hui; Zhang, Hongwu; Zheng, Yonggang A coupling extended multiscale finite element method for dynamic analysis of heterogeneous saturated porous media. (English) Zbl 1352.76060 Int. J. Numer. Methods Eng. 104, No. 1, 18-47 (2015). MSC: 76M10 74S05 65M60 74F10 76S05 PDF BibTeX XML Cite \textit{H. Li} et al., Int. J. Numer. Methods Eng. 104, No. 1, 18--47 (2015; Zbl 1352.76060) Full Text: DOI
Chung, Eric T.; Efendiev, Yalchin; Leung, Wing Tat Residual-driven online generalized multiscale finite element methods. (English) Zbl 1349.65615 J. Comput. Phys. 302, 176-190 (2015). MSC: 65N30 65N55 PDF BibTeX XML Cite \textit{E. T. Chung} et al., J. Comput. Phys. 302, 176--190 (2015; Zbl 1349.65615) Full Text: DOI arXiv
Elfverson, Daniel; Ginting, Victor; Henning, Patrick On multiscale methods in Petrov-Galerkin formulation. (English) Zbl 1330.65187 Numer. Math. 131, No. 4, 643-682 (2015). MSC: 65N55 65N30 65N12 65Y20 35J05 35L65 65M55 65M60 65M12 76T10 76M10 PDF BibTeX XML Cite \textit{D. Elfverson} et al., Numer. Math. 131, No. 4, 643--682 (2015; Zbl 1330.65187) Full Text: DOI arXiv
Henning, Patrick; Ohlberger, Mario; Schweizer, Ben Adaptive heterogeneous multiscale methods for immiscible two-phase flow in porous media. (English) Zbl 1326.76060 Comput. Geosci. 19, No. 1, 99-114 (2015). MSC: 76M10 76S05 76T99 35B27 65N08 65N30 PDF BibTeX XML Cite \textit{P. Henning} et al., Comput. Geosci. 19, No. 1, 99--114 (2015; Zbl 1326.76060) Full Text: DOI arXiv
Owhadi, Houman Bayesian numerical homogenization. (English) Zbl 1322.35002 Multiscale Model. Simul. 13, No. 3, 812-828 (2015). MSC: 35B27 65C50 60H35 35J25 60H30 62C10 PDF BibTeX XML Cite \textit{H. Owhadi}, Multiscale Model. Simul. 13, No. 3, 812--828 (2015; Zbl 1322.35002) Full Text: DOI arXiv
Cortinovis, Davide; Jenny, Patrick Iterative Galerkin-enriched multiscale finite-volume method. (English) Zbl 1349.65576 J. Comput. Phys. 277, 248-267 (2014). MSC: 65N08 PDF BibTeX XML Cite \textit{D. Cortinovis} and \textit{P. Jenny}, J. Comput. Phys. 277, 248--267 (2014; Zbl 1349.65576) Full Text: DOI
Lin, Guang; Liu, Jiangguo; Mu, Lin; Ye, Xiu Weak Galerkin finite element methods for Darcy flow: anisotropy and heterogeneity. (English) Zbl 1349.76234 J. Comput. Phys. 276, 422-437 (2014). MSC: 76M10 65N30 76S05 PDF BibTeX XML Cite \textit{G. Lin} et al., J. Comput. Phys. 276, 422--437 (2014; Zbl 1349.76234) Full Text: DOI
Ghommem, Mehdi; Calo, Victor M.; Efendiev, Yalchin Mode decomposition methods for flows in high-contrast porous media. A global approach. (English) Zbl 1349.76208 J. Comput. Phys. 257, Part A, 400-413 (2014). MSC: 76M10 65M60 76S05 PDF BibTeX XML Cite \textit{M. Ghommem} et al., J. Comput. Phys. 257, Part A, 400--413 (2014; Zbl 1349.76208) Full Text: DOI
Presho, Michael; Protasov, Anastasiya; Gildin, Eduardo Local-global model reduction of parameter-dependent, single-phase flow models via balanced truncation. (English) Zbl 1329.76187 J. Comput. Appl. Math. 271, 163-179 (2014). MSC: 76M10 65M60 35Q35 65M50 76S05 PDF BibTeX XML Cite \textit{M. Presho} et al., J. Comput. Appl. Math. 271, 163--179 (2014; Zbl 1329.76187) Full Text: DOI
Deng, Weibing; Wu, Haijun A combined finite element and multiscale finite element method for the multiscale elliptic problems. (English) Zbl 1400.65057 Multiscale Model. Simul. 12, No. 4, 1424-1457 (2014). MSC: 65N30 34E13 35B27 35J25 65N12 65N15 PDF BibTeX XML Cite \textit{W. Deng} and \textit{H. Wu}, Multiscale Model. Simul. 12, No. 4, 1424--1457 (2014; Zbl 1400.65057) Full Text: DOI arXiv
Ganis, Benjamin; Kumar, Kundan; Pencheva, Gergina; Wheeler, Mary F.; Yotov, Ivan A global Jacobian method for mortar discretizations of a fully implicit two-phase flow model. (English) Zbl 1312.76027 Multiscale Model. Simul. 12, No. 4, 1401-1423 (2014). MSC: 76M10 65M55 65M60 76S05 76T99 PDF BibTeX XML Cite \textit{B. Ganis} et al., Multiscale Model. Simul. 12, No. 4, 1401--1423 (2014; Zbl 1312.76027) Full Text: DOI
Zhang, Yifan; Wang, Wei; Guzmán, Johnny; Shu, Chi-Wang Multi-scale discontinuous Galerkin method for solving elliptic problems with curvilinear unidirectional rough coefficients. (English) Zbl 1307.65171 J. Sci. Comput. 61, No. 1, 42-60 (2014). Reviewer: Constantin Popa (Constanţa) MSC: 65N30 35J25 65N15 65N55 PDF BibTeX XML Cite \textit{Y. Zhang} et al., J. Sci. Comput. 61, No. 1, 42--60 (2014; Zbl 1307.65171) Full Text: DOI
Keppens, Rony; Porth, Oliver Scalar hyperbolic PDE simulations and coupling strategies. (English) Zbl 1293.65113 J. Comput. Appl. Math. 266, 87-101 (2014). MSC: 65M06 PDF BibTeX XML Cite \textit{R. Keppens} and \textit{O. Porth}, J. Comput. Appl. Math. 266, 87--101 (2014; Zbl 1293.65113) Full Text: DOI
Galvis, J.; Kang, S. Ki Spectral multiscale finite element for nonlinear flows in highly heterogeneous media: a reduced basis approach. (English) Zbl 1293.76086 J. Comput. Appl. Math. 260, 494-508 (2014). MSC: 76M10 76S05 65M60 PDF BibTeX XML Cite \textit{J. Galvis} and \textit{S. K. Kang}, J. Comput. Appl. Math. 260, 494--508 (2014; Zbl 1293.76086) Full Text: DOI
Bush, Lawrence; Ginting, Victor; Presho, Michael Application of a conservative, generalized multiscale finite element method to flow models. (English) Zbl 1293.76084 J. Comput. Appl. Math. 260, 395-409 (2014). MSC: 76M10 76Txx PDF BibTeX XML Cite \textit{L. Bush} et al., J. Comput. Appl. Math. 260, 395--409 (2014; Zbl 1293.76084) Full Text: DOI arXiv
Galvis, Juan; Wei, Jia Ensemble level multiscale finite element and preconditioner for channelized systems and applications. (English) Zbl 1291.76199 J. Comput. Appl. Math. 255, 456-467 (2014). MSC: 76M10 76S05 65N55 PDF BibTeX XML Cite \textit{J. Galvis} and \textit{J. Wei}, J. Comput. Appl. Math. 255, 456--467 (2014; Zbl 1291.76199) Full Text: DOI
Zhang, H. W.; Liu, H.; Wu, J. K. A uniform multiscale method for 2D static and dynamic analyses of heterogeneous materials. (English) Zbl 1352.74459 Int. J. Numer. Methods Eng. 93, No. 7, 714-746 (2013). MSC: 74S05 65N30 74L10 PDF BibTeX XML Cite \textit{H. W. Zhang} et al., Int. J. Numer. Methods Eng. 93, No. 7, 714--746 (2013; Zbl 1352.74459) Full Text: DOI
Efendiev, Yalchin; Galvis, Juan; Hou, Thomas Y. Generalized multiscale finite element methods (GMsFEM). (English) Zbl 1349.65617 J. Comput. Phys. 251, 116-135 (2013). MSC: 65N30 PDF BibTeX XML Cite \textit{Y. Efendiev} et al., J. Comput. Phys. 251, 116--135 (2013; Zbl 1349.65617) Full Text: DOI arXiv
Zhang, Na; Yao, Jun; Huang, Zhaoqin; Wang, Yueying Accurate multiscale finite element method for numerical simulation of two-phase flow in fractured media using discrete-fracture model. (English) Zbl 1299.76156 J. Comput. Phys. 242, 420-438 (2013). MSC: 76M10 76T99 74S05 74R10 PDF BibTeX XML Cite \textit{N. Zhang} et al., J. Comput. Phys. 242, 420--438 (2013; Zbl 1299.76156) Full Text: DOI
Casadei, F.; Rimoli, J. J.; Ruzzene, M. A geometric multiscale finite element method for the dynamic analysis of heterogeneous solids. (English) Zbl 1286.74097 Comput. Methods Appl. Mech. Eng. 263, 56-70 (2013). MSC: 74S05 PDF BibTeX XML Cite \textit{F. Casadei} et al., Comput. Methods Appl. Mech. Eng. 263, 56--70 (2013; Zbl 1286.74097) Full Text: DOI
Jiang, Lijian; Efendiev, Yalchin A priori estimates for two multiscale finite element methods using multiple global fields to wave equations. (English) Zbl 1251.65131 Numer. Methods Partial Differ. Equations 28, No. 6, 1869-1892 (2012). MSC: 65M15 65M60 PDF BibTeX XML Cite \textit{L. Jiang} and \textit{Y. Efendiev}, Numer. Methods Partial Differ. Equations 28, No. 6, 1869--1892 (2012; Zbl 1251.65131) Full Text: DOI
Zhang, Jianying; Jiang, Bin Enhanced Euler’s method to a free boundary porous media flow problem. (English) Zbl 1386.76169 Numer. Methods Partial Differ. Equations 28, No. 5, 1558-1573 (2012). MSC: 76S05 76M25 PDF BibTeX XML Cite \textit{J. Zhang} and \textit{B. Jiang}, Numer. Methods Partial Differ. Equations 28, No. 5, 1558--1573 (2012; Zbl 1386.76169) Full Text: DOI
Zhang, H. W.; Wu, J. K.; Lv, J. A new multiscale computational method for elasto-plastic analysis of heterogeneous materials. (English) Zbl 1316.74064 Comput. Mech. 49, No. 2, 149-169 (2012). MSC: 74S05 74C05 74E05 PDF BibTeX XML Cite \textit{H. W. Zhang} et al., Comput. Mech. 49, No. 2, 149--169 (2012; Zbl 1316.74064) Full Text: DOI
Sandvin, Andreas; Nordbotten, Jan Martin; Aavatsmark, Ivar Multiscale mass conservative domain decomposition preconditioners for elliptic problems on irregular grids. (English) Zbl 1348.76162 Comput. Geosci. 15, No. 3, 587-602 (2011). MSC: 76S05 76M25 65F08 PDF BibTeX XML Cite \textit{A. Sandvin} et al., Comput. Geosci. 15, No. 3, 587--602 (2011; Zbl 1348.76162) Full Text: DOI
He, J.; Sætrom, J.; Durlofsky, L. J. Enhanced linearized reduced-order models for subsurface flow simulation. (English) Zbl 1337.76064 J. Comput. Phys. 230, No. 23, 8313-8341 (2011). MSC: 76S05 76M25 76T99 PDF BibTeX XML Cite \textit{J. He} et al., J. Comput. Phys. 230, No. 23, 8313--8341 (2011; Zbl 1337.76064) Full Text: DOI
Efendiev, Yalchin; Galvis, Juan; Wu, Xiao-Hui Multiscale finite element methods for high-contrast problems using local spectral basis functions. (English) Zbl 1391.76321 J. Comput. Phys. 230, No. 4, 937-955 (2011). MSC: 76M10 65M60 76S05 PDF BibTeX XML Cite \textit{Y. Efendiev} et al., J. Comput. Phys. 230, No. 4, 937--955 (2011; Zbl 1391.76321) Full Text: DOI
Zhang, Hong-Wu; Wu, Jing-Kai; Lü, Jun; Fu, Zhen-Dong Extended multiscale finite element method for mechanical analysis of heterogeneous materials. (English) Zbl 1270.74196 Acta Mech. Sin. 26, No. 6, 899-920 (2010). MSC: 74S05 74E05 PDF BibTeX XML Cite \textit{H.-W. Zhang} et al., Acta Mech. Sin. 26, No. 6, 899--920 (2010; Zbl 1270.74196) Full Text: DOI
Chueh, C. C.; Secanell, M.; Bangerth, W.; Djilali, N. Multi-level adaptive simulation of transient two-phase flow in heterogeneous porous media. (English) Zbl 1245.76047 Comput. Fluids 39, No. 9, 1585-1596 (2010). MSC: 76M10 76S05 76T10 PDF BibTeX XML Cite \textit{C. C. Chueh} et al., Comput. Fluids 39, No. 9, 1585--1596 (2010; Zbl 1245.76047) Full Text: DOI
Jiang, L.; Mishev, I.; Li, Y. Stochastic mixed multiscale finite element methods and their applications in random porous media. (English) Zbl 1231.74418 Comput. Methods Appl. Mech. Eng. 199, No. 41-44, 2721-2740 (2010). MSC: 74S05 74S60 74F10 74E35 PDF BibTeX XML Cite \textit{L. Jiang} et al., Comput. Methods Appl. Mech. Eng. 199, No. 41--44, 2721--2740 (2010; Zbl 1231.74418) Full Text: DOI
Berlyand, Leonid; Owhadi, Houman Flux norm approach to finite-dimensional homogenization approximations with non-separated scales and high contrast. (English) Zbl 1229.35009 Arch. Ration. Mech. Anal. 198, No. 2, 677-721 (2010). Reviewer: Alain Brillard (Riedisheim) MSC: 35B27 49J45 65N30 74Q05 35J25 35J57 PDF BibTeX XML Cite \textit{L. Berlyand} and \textit{H. Owhadi}, Arch. Ration. Mech. Anal. 198, No. 2, 677--721 (2010; Zbl 1229.35009) Full Text: DOI arXiv
Jiang, Lijian; Efendiev, Yalchin; Ginting, Victor Analysis of global multiscale finite element methods for wave equations with continuum spatial scales. (English) Zbl 1205.65270 Appl. Numer. Math. 60, No. 8, 862-876 (2010). Reviewer: Petr Sváček (Praha) MSC: 65M60 35L05 65M12 PDF BibTeX XML Cite \textit{L. Jiang} et al., Appl. Numer. Math. 60, No. 8, 862--876 (2010; Zbl 1205.65270) Full Text: DOI
Zhang, H. W.; Wu, J. K.; Fu, Z. D. Extended multiscale finite element method for elasto-plastic analysis of 2D periodic lattice truss materials. (English) Zbl 1398.74429 Comput. Mech. 45, No. 6, 623-635 (2010). MSC: 74S05 76S05 74E05 74E30 76M10 PDF BibTeX XML Cite \textit{H. W. Zhang} et al., Comput. Mech. 45, No. 6, 623--635 (2010; Zbl 1398.74429) Full Text: DOI
Jiang, Lijian; Efendiev, Yalchin; Mishev, Iiya Mixed multiscale finite element methods using approximate global information based on partial upscaling. (English) Zbl 1187.65129 Comput. Geosci. 14, No. 2, 319-341 (2010). Reviewer: Wilhelm Heinrichs (Essen) MSC: 65N30 35B27 76M50 76S05 76M10 76T10 65N12 65N15 PDF BibTeX XML Cite \textit{L. Jiang} et al., Comput. Geosci. 14, No. 2, 319--341 (2010; Zbl 1187.65129) Full Text: DOI
Chen, Tianhong; Gerritsen, Margot G.; Lambers, James V.; Durlofsky, Louis J. Global variable compact multipoint methods for accurate upscaling with full-tensor effects. (English) Zbl 1398.76169 Comput. Geosci. 14, No. 1, 65-81 (2010). MSC: 76M25 PDF BibTeX XML Cite \textit{T. Chen} et al., Comput. Geosci. 14, No. 1, 65--81 (2010; Zbl 1398.76169) Full Text: DOI
Sviercoski, R. F.; Popov, P.; Travis, B. J. Zeroth and first-order homogenized approximations to nonlinear diffusion through block inclusions by an analytical approach. (English) Zbl 1229.76086 Comput. Methods Appl. Mech. Eng. 198, No. 30-32, 2260-2271 (2009). MSC: 76M50 76R50 76S05 PDF BibTeX XML Cite \textit{R. F. Sviercoski} et al., Comput. Methods Appl. Mech. Eng. 198, No. 30--32, 2260--2271 (2009; Zbl 1229.76086) Full Text: DOI
Hajibeygi, Hadi; Jenny, Patrick Multiscale finite-volume method for parabolic problems arising from compressible multiphase flow in porous media. (English) Zbl 1280.76019 J. Comput. Phys. 228, No. 14, 5129-5147 (2009). MSC: 76M12 65M08 76S05 76T10 PDF BibTeX XML Cite \textit{H. Hajibeygi} and \textit{P. Jenny}, J. Comput. Phys. 228, No. 14, 5129--5147 (2009; Zbl 1280.76019) Full Text: DOI
Ganapathysubramanian, B.; Zabaras, N. A stochastic multiscale framework for modeling flow through random heterogeneous porous media. (English) Zbl 1409.76139 J. Comput. Phys. 228, No. 2, 591-618 (2009). MSC: 76S05 76M35 65C30 PDF BibTeX XML Cite \textit{B. Ganapathysubramanian} and \textit{N. Zabaras}, J. Comput. Phys. 228, No. 2, 591--618 (2009; Zbl 1409.76139) Full Text: DOI
Ganapathysubramanian, Basked; Zabaras, Nicholas Modeling multiscale diffusion processes in random heterogeneous media. (English) Zbl 1194.74052 Comput. Methods Appl. Mech. Eng. 197, No. 43-44, 3560-3573 (2008). MSC: 74F05 74S60 80A20 PDF BibTeX XML Cite \textit{B. Ganapathysubramanian} and \textit{N. Zabaras}, Comput. Methods Appl. Mech. Eng. 197, No. 43--44, 3560--3573 (2008; Zbl 1194.74052) Full Text: DOI
Dostert, P.; Efendiev, Y.; Hou, T. Y. Multiscale finite element methods for stochastic porous media flow equations and application to uncertainty quantification. (English) Zbl 1194.76112 Comput. Methods Appl. Mech. Eng. 197, No. 43-44, 3445-3455 (2008). MSC: 76M10 76S05 76M35 PDF BibTeX XML Cite \textit{P. Dostert} et al., Comput. Methods Appl. Mech. Eng. 197, No. 43--44, 3445--3455 (2008; Zbl 1194.76112) Full Text: DOI
Kippe, Vegard; Aarnes, Jørg E.; Lie, Knut-Andreas A comparison of multiscale methods for elliptic problems in porous media flow. (English) Zbl 1259.76047 Comput. Geosci. 12, No. 3, 377-398 (2008). MSC: 76M25 76S05 76T10 PDF BibTeX XML Cite \textit{V. Kippe} et al., Comput. Geosci. 12, No. 3, 377--398 (2008; Zbl 1259.76047) Full Text: DOI
Efendiev, Yalchin R.; Hou, Thomas Yizhao; Strinopoulos, T. Multiscale simulations of porous media flows in flow-based coordinate system. (English) Zbl 1155.76050 Comput. Geosci. 12, No. 3, 257-272 (2008). MSC: 76M50 76S05 76M10 76T10 PDF BibTeX XML Cite \textit{Y. R. Efendiev} et al., Comput. Geosci. 12, No. 3, 257--272 (2008; Zbl 1155.76050) Full Text: DOI
Hajibeygi, Hadi; Bonfigli, Giuseppe; Hesse, Marc Andre; Jenny, Patrick Iterative multiscale finite-volume method. (English) Zbl 1151.65091 J. Comput. Phys. 227, No. 19, 8604-8621 (2008). MSC: 65N30 35J25 35J05 65N12 65N15 76M12 76T30 76S05 PDF BibTeX XML Cite \textit{H. Hajibeygi} et al., J. Comput. Phys. 227, No. 19, 8604--8621 (2008; Zbl 1151.65091) Full Text: DOI
Lipnikov, K.; Moulton, J. D.; Svyatskiy, D. A multilevel multiscale mimetic (M\(^3\)) method for two-phase flows in porous media. (English) Zbl 1338.76096 J. Comput. Phys. 227, No. 14, 6727-6753 (2008). MSC: 76M25 76S05 76T99 PDF BibTeX XML Cite \textit{K. Lipnikov} et al., J. Comput. Phys. 227, No. 14, 6727--6753 (2008; Zbl 1338.76096) Full Text: DOI
Efendiev, Yalchin R.; Hou, Thomas Yizhao Multiscale finite element methods for porous media flows and their applications. (English) Zbl 1112.76046 Appl. Numer. Math. 57, No. 5-7, 577-596 (2007). MSC: 76M10 76S05 PDF BibTeX XML Cite \textit{Y. R. Efendiev} and \textit{T. Y. Hou}, Appl. Numer. Math. 57, No. 5--7, 577--596 (2007; Zbl 1112.76046) Full Text: DOI
Velamur Asokan, Badrinarayanan; Zabaras, Nicholas A stochastic variational multiscale method for diffusion in heterogeneous random media. (English) Zbl 1106.65004 J. Comput. Phys. 218, No. 2, 654-676 (2006). MSC: 65C30 60H15 35R60 65N30 65N55 PDF BibTeX XML Cite \textit{B. Velamur Asokan} and \textit{N. Zabaras}, J. Comput. Phys. 218, No. 2, 654--676 (2006; Zbl 1106.65004) Full Text: DOI