Liu, Xinliang; Chung, Eric; Zhang, Lei Iterated numerical homogenization for multiscale elliptic equations with monotone nonlinearity. (English) Zbl 1478.65128 Multiscale Model. Simul. 19, No. 4, 1601-1632 (2021). MSC: 65N30 PDFBibTeX XMLCite \textit{X. Liu} et al., Multiscale Model. Simul. 19, No. 4, 1601--1632 (2021; Zbl 1478.65128) Full Text: DOI arXiv
Verfürth, Barbara Heterogeneous multiscale method for the Maxwell equations with high contrast. (English) Zbl 1422.65415 ESAIM, Math. Model. Numer. Anal. 53, No. 1, 35-61 (2019). MSC: 65N30 65N15 65N12 35Q61 78M40 35B27 78A45 PDFBibTeX XMLCite \textit{B. Verfürth}, ESAIM, Math. Model. Numer. Anal. 53, No. 1, 35--61 (2019; Zbl 1422.65415) Full Text: DOI arXiv
Tan, Wee Chin; Hoang, Viet Ha High dimensional finite element method for multiscale nonlinear monotone parabolic equations. (English) Zbl 1402.65118 J. Comput. Appl. Math. 345, 471-500 (2019). MSC: 65M60 35K55 65M15 15A72 PDFBibTeX XMLCite \textit{W. C. Tan} and \textit{V. H. Hoang}, J. Comput. Appl. Math. 345, 471--500 (2019; Zbl 1402.65118) Full Text: DOI
Nouy, Anthony; Pled, Florent A multiscale method for semi-linear elliptic equations with localized uncertainties and non-linearities. (English) Zbl 1479.35971 ESAIM, Math. Model. Numer. Anal. 52, No. 5, 1763-1802 (2018). MSC: 35R60 35J62 35J66 60H15 65N30 65N55 65D15 PDFBibTeX XMLCite \textit{A. Nouy} and \textit{F. Pled}, ESAIM, Math. Model. Numer. Anal. 52, No. 5, 1763--1802 (2018; Zbl 1479.35971) Full Text: DOI arXiv
Chung, Eric; Efendiev, Yalchin; Shi, Ke; Ye, Shuai A multiscale model reduction method for nonlinear monotone elliptic equations in heterogeneous media. (English) Zbl 1377.65148 Netw. Heterog. Media 12, No. 4, 619-642 (2017). MSC: 65N30 35J92 65N12 PDFBibTeX XMLCite \textit{E. Chung} et al., Netw. Heterog. Media 12, No. 4, 619--642 (2017; Zbl 1377.65148) Full Text: DOI
Abdulle, Assyr Numerical homogenization methods for parabolic monotone problems. (English) Zbl 1357.65168 Barrenechea, Gabriel R. (ed.) et al., Building bridges: connections and challenges in modern approaches to numerical partial differential equations. Selected papers based on the presentations at the 101st LMS-EPSRC symposium, Durham, UK, July 8–16, 2014. Cham: Springer (ISBN 978-3-319-41638-0/hbk; 978-3-319-41640-3/ebook). Lecture Notes in Computational Science and Engineering 114, 1-38 (2016). MSC: 65M60 65M20 35K55 65L06 35B27 65M12 PDFBibTeX XMLCite \textit{A. Abdulle}, Lect. Notes Comput. Sci. Eng. 114, 1--38 (2016; Zbl 1357.65168) Full Text: DOI Link
Abdulle, Assyr; Huber, Martin E. Finite element heterogeneous multiscale method for nonlinear monotone parabolic homogenization problems. (English) Zbl 1357.65169 ESAIM, Math. Model. Numer. Anal. 50, No. 6, 1659-1697 (2016). Reviewer: H. P. Dikshit (Bhopal) MSC: 65M60 74Q10 74D10 35K55 35B27 65M55 65M15 35Q74 PDFBibTeX XMLCite \textit{A. Abdulle} and \textit{M. E. Huber}, ESAIM, Math. Model. Numer. Anal. 50, No. 6, 1659--1697 (2016; Zbl 1357.65169) Full Text: DOI Link
Frénod, Emmanuel (ed.) Preface: Homogenization-Based Numerical Methods. (English) Zbl 1388.76003 Discrete Contin. Dyn. Syst., Ser. S 9, No. 5, i-ix (2016). MSC: 76-03 01A61 76M50 76X05 82D10 82C80 PDFBibTeX XMLCite \textit{E. Frénod} (ed.), Discrete Contin. Dyn. Syst., Ser. S 9, No. 5, i-ix (2016; Zbl 1388.76003) Full Text: DOI
Henning, Patrick; Ohlberger, Mario A-posteriori error estimate for a heterogeneous multiscale approximation of advection-diffusion problems with large expected drift. (English) Zbl 1357.65147 Discrete Contin. Dyn. Syst., Ser. S 9, No. 5, 1393-1420 (2016). MSC: 65M15 65M60 35K15 35B27 65M50 PDFBibTeX XMLCite \textit{P. Henning} and \textit{M. Ohlberger}, Discrete Contin. Dyn. Syst., Ser. S 9, No. 5, 1393--1420 (2016; Zbl 1357.65147) Full Text: DOI
Abdulle, Assyr; Huber, Martin E. Error estimates for finite element approximations of nonlinear monotone elliptic problems with application to numerical homogenization. (English) Zbl 1350.65112 Numer. Methods Partial Differ. Equations 32, No. 3, 955-969 (2016). Reviewer: Tomas Vejchodsky (Praha) MSC: 65N15 65N30 35J60 PDFBibTeX XMLCite \textit{A. Abdulle} and \textit{M. E. Huber}, Numer. Methods Partial Differ. Equations 32, No. 3, 955--969 (2016; Zbl 1350.65112) Full Text: DOI Link
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 PDFBibTeX XMLCite \textit{P. Henning} et al., Comput. Geosci. 19, No. 1, 99--114 (2015; Zbl 1326.76060) Full Text: DOI arXiv
Frénod, Emmanuel An attempt at classifying homogenization-based numerical methods. (English) Zbl 1304.65184 Discrete Contin. Dyn. Syst., Ser. S 8, No. 1, i-vi (2015). MSC: 65L99 65M99 65N99 34E10 35B27 35B40 PDFBibTeX XMLCite \textit{E. Frénod}, Discrete Contin. Dyn. Syst., Ser. S 8, No. 1, i-vi (2015; Zbl 1304.65184) Full Text: DOI