Dobson, Matthew There is no pointwise consistent quasicontinuum energy. (English) Zbl 1305.82044 IMA J. Numer. Anal. 34, No. 4, 1541-1553 (2014). MSC: 82C24 81V45 74A60 74A25 PDFBibTeX XMLCite \textit{M. Dobson}, IMA J. Numer. Anal. 34, No. 4, 1541--1553 (2014; Zbl 1305.82044) Full Text: DOI arXiv
Dobson, M.; Ortner, C.; Shapeev, A. V. The spectrum of the force-based quasicontinuum operator for a homogeneous periodic chain. (English) Zbl 1257.82106 Multiscale Model. Simul. 10, No. 3, 744-765 (2012). MSC: 82D20 65N12 65N15 70C20 PDFBibTeX XMLCite \textit{M. Dobson} et al., Multiscale Model. Simul. 10, No. 3, 744--765 (2012; Zbl 1257.82106) Full Text: DOI arXiv
Dobson, M.; Luskin, M.; Ortner, C. Iterative methods for the force-based quasicontinuum approximation: analysis of a 1D model problem. (English) Zbl 1230.74222 Comput. Methods Appl. Mech. Eng. 200, No. 37-40, 2697-2709 (2011). MSC: 74S30 74A25 PDFBibTeX XMLCite \textit{M. Dobson} et al., Comput. Methods Appl. Mech. Eng. 200, No. 37--40, 2697--2709 (2011; Zbl 1230.74222) Full Text: DOI arXiv Link
Dobson, M.; Luskin, M.; Ortner, C. Accuracy of quasicontinuum approximations near instabilities. (English) Zbl 1200.74005 J. Mech. Phys. Solids 58, No. 10, 1741-1757 (2010). MSC: 74A25 74G60 PDFBibTeX XMLCite \textit{M. Dobson} et al., J. Mech. Phys. Solids 58, No. 10, 1741--1757 (2010; Zbl 1200.74005) Full Text: DOI arXiv
Dobson, M.; Luskin, M.; Ortner, C. Sharp stability estimates for the force-based quasicontinuum approximation of homogeneous tensile deformation. (English) Zbl 1225.82009 Multiscale Model. Simul. 8, No. 3, 782-802 (2010). MSC: 82B20 65Z05 70C20 82D25 PDFBibTeX XMLCite \textit{M. Dobson} et al., Multiscale Model. Simul. 8, No. 3, 782--802 (2010; Zbl 1225.82009) Full Text: DOI arXiv Link
Dobson, Matthew; Luskin, Mitchell; Ortner, Christoph Stability, instability, and error of the force-based quasicontinuum approximation. (English) Zbl 1268.74006 Arch. Ration. Mech. Anal. 197, No. 1, 179-202 (2010). Reviewer: I. A. Parinov (Rostov-na-Donu) MSC: 74A25 82B21 PDFBibTeX XMLCite \textit{M. Dobson} et al., Arch. Ration. Mech. Anal. 197, No. 1, 179--202 (2010; Zbl 1268.74006) Full Text: DOI arXiv
Dobson, Matthew; Luskin, Mitchell An optimal order error analysis of the one-dimensional quasicontinuum approximation. (English) Zbl 1203.82089 SIAM J. Numer. Anal. 47, No. 4, 2455-2475 (2009). Reviewer: Farruh Mukhamedov (Kuantan) MSC: 82D20 82D25 82B21 70C20 PDFBibTeX XMLCite \textit{M. Dobson} and \textit{M. Luskin}, SIAM J. Numer. Anal. 47, No. 4, 2455--2475 (2009; Zbl 1203.82089) Full Text: DOI arXiv
Dobson, Matthew; Luskin, Mitchell Iterative solution of the quasicontinuum equilibrium equations with continuation. (English) Zbl 1203.65085 J. Sci. Comput. 37, No. 1, 19-41 (2008). MSC: 65H10 74A25 74A45 82B80 PDFBibTeX XMLCite \textit{M. Dobson} and \textit{M. Luskin}, J. Sci. Comput. 37, No. 1, 19--41 (2008; Zbl 1203.65085) Full Text: DOI arXiv
Dobson, Matthew; Luskin, Mitchell Analysis of a force-based quasicontinuum approximation. (English) Zbl 1140.74006 ESAIM, Math. Model. Numer. Anal. 42, No. 1, 113-139 (2008). MSC: 74A25 82B21 PDFBibTeX XMLCite \textit{M. Dobson} and \textit{M. Luskin}, ESAIM, Math. Model. Numer. Anal. 42, No. 1, 113--139 (2008; Zbl 1140.74006) Full Text: DOI arXiv EuDML