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Publications

Submitted

  1. A. Abdulle, P. Lin, and A. V. Shapeev. A priori and a posteriori W1, infty error analysis of a QC method for complex lattices. arXiv:1104.0311.

  2. C. Ortner and A. V. Shapeev. Analysis of an energy-based atomistic/continuum coupling approximation of a vacancy in the 2D triangular lattice. arXiv:1104.0311.

Published

  1. A. Abdulle, P. Lin, and A. V. Shapeev. Numerical methods for multilattices. Multiscale Model. Simul., 10(3): 696–726, 2012. arXiv:1107.3462.

  2. M. Dobson, C. Ortner, and A. V. Shapeev. The spectrum of the force-based quasicontinuum operator for a homogeneous periodic chain. Multiscale Model. Simul., 10(3): 744–765, 2012. arXiv:1004.3435.

  3. A. V. Shapeev. Consistent energy-based atomistic/continuum coupling for two-body potentials in three dimensions. SIAM J. Sci. Comput., 34(3):B335–B360, 2012. arXiv:1108.2991.

  4. A. V. Shapeev. Consistent energy-based atomistic/continuum coupling for two-body potentials in one and two dimensions. Multiscale Model. Simul., 9(3): 905–932, 2011. arXiv:1010.0512.

  5. A. V. Shapeev and Ping Lin. An asymptotic fitting finite element method with exponential mesh refinement for accurate computation of corner eddies in viscous flows. SIAM J. Sci. Comput., 31(3): 1874–1900, 2009.

  6. A. V. Shapeev. Investigation of mixed spectral and finite difference approximation on the basis of problem of viscous flow in a diffuser. Siberian Journal of Numerical Mathematics, 8(2): 149–162, 2005. in Russian.

  7. A. V. Shapeev. Unsteady self-similar flow of a viscous incompressible fluid in a plane divergent channel. Fluid Dynamics, 39(1): 36–41, 2004.

  8. A. V. Shapeev and V. P. Shapeev. High-order accurate difference schemes for elliptic equations in a domain with a curvilinear boundary. Computational Mathematics and Mathematical Physics, 40(2): 213–221, 2000.

Proceedings and Preprints

  1. C. Ortner and A. V. Shapeev. Interpolants of lattice functions for the analysis of atomistic/continuum multiscale methods, 2012. arXiv:1204.3705.

  2. A. Abdulle, P. Lin, and A. V. Shapeev. Homogenization-based analysis of quasicontinuum method for complex crystals, 2010. arXiv:1006.0378.

  3. Gilles Carre, Stephane Del Pino, Kirill Pichon Gostaf, Emmanuel Labourasse, and Alexander Shapeev. Polynomial least-squares reconstruction for semi-lagrangian cell-centered hydrodynamic schemes. In ESAIM Proceedings, CEMRACS 2008 - Modelling and Numerical Simulation of Complex Fluids, volume 28, pages 100–116, 2009.

  4. A. V. Shapeev. Viscous incompressible axisymmetric flows in cones. Preprint 2-09, Lavrentyev Institute of Hydrodynamics SB RAS, 2009. In Russian.

  5. A. V. Shapeev. A numerical-asymptotic method for computation of infinite number of eddies of viscous flows in domains with corners. In Computational Fluid Dynamics, 2008.

  6. G. Czichowski, A. V. Shapeev, and V. P Shapeev. Pattern formation – group theoretical and numerical points of view. Preprint 15/2002, Ernst-Moritz-Arndt-Universitat Greifswald, Institut fur Mathematik und Informatik, 2002.

  7. A. V. Shapeev. Numerical simulation of 3d motions of locally heated liquid films. In Proceedings of the Third Russian National Conference on Heat Transfer, pages 103–105, Moscow, Russia, October 2002. in Russian.

  8. A. V. Shapeev. Proof of convergence of numerical methods of solving weakly nonlinear problems. In Problems of Continuous Media Mechanics: Proceedings of the 33rd Regional Youth Conference, pages 189–193, Ekaterinburg, Russia, 2002. in Russian.

  9. A. V. Shapeev. Unconditionally stable explicit high-order scheme for the nonlinear schrodinger equation. In Proceedings of the Youth Scientific Conference dedicated to the 10th anniversary of Institute of Computational Technologies SB RAS, volume 2, pages 175–179, Novosibirsk, Russia, 2001. in Russian.

  10. A. V. Shapeev and V. P. Shapeev. Solution of elliptical problems with singularities using high-order schemes. In Problems of Continuous Media Mechanics: Proceedings of the 32nd Regional Youth Conference, pages 62–66, Ekaterinburg, Russia, 2001. in Russian.

  11. A. V. Shapeev and V. P. Shapeev. High order approximation schemes. In Proceedings of the 3rd European Conference on Numerical Mathematics and Advanced Applications, pages 715–724. World Scientific, 2000.

  12. P. Lin and A. V. Shapeev. Energy-based ghost force removing techniques for the quasicontinuum method. arXiv:0909.5437.

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