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, Assyr; Pouchon, Timothée A priori error analysis of the finite element heterogeneous multiscale method for the wave equation over long time. (English) Zbl 1382.65303 SIAM J. Numer. Anal. 54, No. 3, 1507-1534 (2016). MSC: 65M60 65M15 35B27 35B10 35B40 35L05 74Q10 74Q15 PDFBibTeX XMLCite \textit{A. Abdulle} and \textit{T. Pouchon}, SIAM J. Numer. Anal. 54, No. 3, 1507--1534 (2016; Zbl 1382.65303) Full Text: DOI
Abdulle, Assyr; Bai, Yun Adaptive reduced basis finite element heterogeneous multiscale method. (English) Zbl 1286.74088 Comput. Methods Appl. Mech. Eng. 257, 203-220 (2013). MSC: 74Q20 74S05 65N30 35B27 PDFBibTeX XMLCite \textit{A. Abdulle} and \textit{Y. Bai}, Comput. Methods Appl. Mech. Eng. 257, 203--220 (2013; Zbl 1286.74088) Full Text: DOI Link