Abstract
This paper gives numerical experiments for the Finite Element Heterogeneous Multiscale Method applied to problems in linear elasticity, which has been analyzed in Abdulle (Math Models Methods Appl Sci 16:615–635, 2006). The main results for the FE-HMM a priori errors are stated and their sharpness are verified though numerical experiments.
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References
A. Abdulle, Analysis of a heterogeneous multiscale FEM for problems in elasticity. Math. Models Methods Appl. Sci. 16 (4), 615–635 (2006)
A. Abdulle, The finite element heterogeneous multiscale method: a computational strategy for multiscale PDEs, in Multiple Scales Problems in Biomathematics, Mechanics, Physics and Numerics. GAKUTO International Series. Mathematical Sciences and Applications, vol. 31 (Gakkōtosho, Tokyo, 2009), pp. 133–181
A. Abdulle, A priori and a posteriori error analysis for numerical homogenization: a unified framework. Ser. Contemp. Appl. Math. CAM 16, 280–305 (2011)
A. Abdulle, Discontinuous Galerkin finite element heterogeneous multiscale method for elliptic problems with multiple scales. Math. Comput. 81 (278), 687–713 (2012)
G. Allaire, Shape Optimization by the Homogenization Method. Applied Mathematical Sciences, vol. 146 (Springer, New York, 2002)
D. Cioranescu, P. Donato, An introduction to homogenization. Oxford Lecture Series in Mathematics and its Applications, vol. 17 (Oxford University Press, New York, 1999)
A. Gloria, Z. Habibi, Reduction of the resonance error – part 2: approximation of correctors, extrapolation, and spectral theory, Preprint, hal-00933234 (2014)
F. Murat, L. Tartar, H-convergence, in Topics in the Mathematical Modelling of Composite Materials. Progress in Nonlinear Differential Equations and Their Applications, vol. 31 (Birkhäuser Boston, Boston, 1997), pp. 21–43
O.A. Oleinik, A. Shamaev, G. Yosifian, Mathematical problems in elasticity and homogenization (North-Holland, Amsterdam, 1992)
G.C. Papanicolaou, S.R.S. Varadhan, Boundary value problems with rapidly oscillating random coefficients, in Random Fields, vol. I, II (Esztergom, 1979). Colloq. Math. Soc. János Bolyai, vol. 27 (North-Holland, Amsterdam/New York, 1981), pp. 835–873
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This work was supported in part by the Swiss National Science Foundation.
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Jecker, O., Abdulle, A. (2016). Numerical Experiments for Multiscale Problems in Linear Elasticity. In: Karasözen, B., Manguoğlu, M., Tezer-Sezgin, M., Göktepe, S., Uğur, Ö. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2015. Lecture Notes in Computational Science and Engineering, vol 112. Springer, Cham. https://doi.org/10.1007/978-3-319-39929-4_13
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DOI: https://doi.org/10.1007/978-3-319-39929-4_13
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