Abdulle, Assyr; Arjmand, Doghonay; Paganoni, Edoardo A parabolic local problem with exponential decay of the resonance error for numerical homogenization. (English) Zbl 07466873 Math. Models Methods Appl. Sci. 31, No. 13, 2733-2772 (2021). MSC: 65-XX 35B27 76M50 35K20 65L70 PDFBibTeX XMLCite \textit{A. Abdulle} et al., Math. Models Methods Appl. Sci. 31, No. 13, 2733--2772 (2021; Zbl 07466873) Full Text: DOI arXiv
Abdulle, A.; Huber, M. E. Numerical homogenization method for parabolic advection-diffusion multiscale problems with large compressible flows. (English) Zbl 1397.76118 Numer. Math. 136, No. 3, 603-649 (2017). MSC: 76M50 76M10 65M60 35K15 65M12 74Q10 76Nxx PDFBibTeX XMLCite \textit{A. Abdulle} and \textit{M. E. Huber}, Numer. Math. 136, No. 3, 603--649 (2017; Zbl 1397.76118) Full Text: DOI
Abdulle, Assyr; Budáč, Ondrej Multiscale model reduction methods for flow in heterogeneous porous media. (English) Zbl 1387.76045 Karasözen, Bülent (ed.) et al., Numerical mathematics and advanced applications – ENUMATH 2015. Selected papers based on the presentations at the European conference, Ankara, Turkey, September 14–18, 2015. Cham: Springer (ISBN 978-3-319-39927-0/hbk; 978-3-319-39929-4/ebook). Lecture Notes in Computational Science and Engineering 112, 333-349 (2016). MSC: 76M10 65N30 76D07 76M50 76S05 PDFBibTeX XMLCite \textit{A. Abdulle} and \textit{O. Budáč}, Lect. Notes Comput. Sci. Eng. 112, 333--349 (2016; Zbl 1387.76045) Full Text: DOI Link
Abdulle, Assyr; Vilmart, Gilles Coupling heterogeneous multiscale FEM with Runge-Kutta methods for parabolic homogenization problems: a fully discrete spacetime analysis. (English) Zbl 1426.76208 Math. Models Methods Appl. Sci. 22, No. 6, Paper No. 2, 40 p. (2012). MSC: 76M10 76M20 76M50 65M12 65M15 PDFBibTeX XMLCite \textit{A. Abdulle} and \textit{G. Vilmart}, Math. Models Methods Appl. Sci. 22, No. 6, Paper No. 2, 40 p. (2012; Zbl 1426.76208) Full Text: DOI
Abdulle, Assyr A priori and a posteriori error analysis for numerical homogenization: a unified framework. (English) Zbl 1300.65076 Damlamian, Alain (ed.) et al., Multiscale problems. Theory, numerical approximation and applications. Selected papers based on the presentations at the ISFMA symposium, Shanghai, China, May 4–16, 2009. Hackensack, NJ: World Scientific; Beijing: Higher Education Press (ISBN 978-981-4366-88-5/hbk; 978-981-4366-89-2/ebook). Series in Contemporary Applied Mathematics CAM 16, 280-305 (2011). MSC: 65N15 65N30 35B27 76M50 74Q05 PDFBibTeX XMLCite \textit{A. Abdulle}, Ser. Contemp. Appl. Math. CAM 16, 280--305 (2011; Zbl 1300.65076)
Abdulle, Assyr; Attinger, Sabine Homogenization method for transport of DNA particles in heterogeneous arrays. (English) Zbl 1140.92300 Attinger, Sabine (ed.) et al., Multiscale modelling and simulation. Proceedings of the summer workshop, Lugano, Switzerland, August 4–30, 2003. Berlin: Springer (ISBN 3-540-21180-2/pbk). Lecture Notes in Computational Science and Engineering 39, 23–33, 269-271 (2004). MSC: 92C05 76M50 35Q92 92C40 76R50 82C70 PDFBibTeX XMLCite \textit{A. Abdulle} and \textit{S. Attinger}, Lect. Notes Comput. Sci. Eng. 39, 23--33, 269--271 (2004; Zbl 1140.92300)