A Priori and A Posteriori $W^{1,\infty}$ Error Analysis of a QC Method for Complex Lattices

DOI10.1137/120894300zbMath1279.65126arXiv1210.2076OpenAlexW2593233103MaRDI QIDQ2855111

Ping Lin, Assyr Abdulle, Alexander V. Shapeev

Publication date: 24 October 2013

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.2076

zbMATH Keywords

convergencenumerical resultsequilibriuminf-sup conditionmultiscale methodquasicontinuum methodmultilatticea priori and a posteriori error analysisatomistic crystalline material

Mathematics Subject Classification ID

Statistical mechanics of crystals (82D25) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Classical equilibrium statistical mechanics (general) (82B05) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) PDEs in connection with statistical mechanics (35Q82)

Related Items (5)

Force-based atomistic/continuum blending for multilattices ⋮ A Posteriori Error Estimation and Adaptive Algorithm for Atomistic/Continuum Coupling in Two Dimensions ⋮ An efficient multigrid strategy for large-scale molecular mechanics optimization ⋮ Adaptive QM/MM coupling for crystalline defects ⋮ An Atomistic/Continuum Coupling Method Using Enriched Bases

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