A-priori analysis of the quasicontinuum method in one dimension
The quasicontinuum method is a coarse-graining technique for reducing the complexity of atomistic simulations in a static and quasistatic setting. In this paper we give an a-priori error analysis for the quasicontinuum method in one dimension. We consider atomistic models with Lennard-Jones type lon...
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| Format: | Report |
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Unspecified
2006
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| _version_ | 1797105648712810496 |
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| author | Ortner, C Suli, E |
| author_facet | Ortner, C Suli, E |
| author_sort | Ortner, C |
| collection | OXFORD |
| description | The quasicontinuum method is a coarse-graining technique for reducing the complexity of atomistic simulations in a static and quasistatic setting. In this paper we give an a-priori error analysis for the quasicontinuum method in one dimension. We consider atomistic models with Lennard-Jones type long range interactions and a practical QC formulation. First, we prove the existence, the local uniqueness and the stability with respect to discrete W1,∞-norm of elastic and fractured atomistic solutions. We then used a fixed point technique to prove the existence of quasicontinuum approximation which satisfies an optimal a-priori error bound. The first-named author acknowledges the financial support received from the European research project HPRN-CT-2002-00284: New Materials, Adaptive Systems and their Nonlinearities. Modelling, Control and Numerical Simulation, and the kind hospitality of Carlo Lovadina (University of Pavia). |
| first_indexed | 2024-03-07T06:50:19Z |
| format | Report |
| id | oxford-uuid:fc58eb1a-fa0f-440c-8fdf-4a757ed1f76c |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:50:19Z |
| publishDate | 2006 |
| publisher | Unspecified |
| record_format | dspace |
| spelling | oxford-uuid:fc58eb1a-fa0f-440c-8fdf-4a757ed1f76c2022-03-27T13:19:58ZA-priori analysis of the quasicontinuum method in one dimensionReporthttp://purl.org/coar/resource_type/c_93fcuuid:fc58eb1a-fa0f-440c-8fdf-4a757ed1f76cMathematical Institute - ePrintsUnspecified2006Ortner, CSuli, EThe quasicontinuum method is a coarse-graining technique for reducing the complexity of atomistic simulations in a static and quasistatic setting. In this paper we give an a-priori error analysis for the quasicontinuum method in one dimension. We consider atomistic models with Lennard-Jones type long range interactions and a practical QC formulation. First, we prove the existence, the local uniqueness and the stability with respect to discrete W1,∞-norm of elastic and fractured atomistic solutions. We then used a fixed point technique to prove the existence of quasicontinuum approximation which satisfies an optimal a-priori error bound. The first-named author acknowledges the financial support received from the European research project HPRN-CT-2002-00284: New Materials, Adaptive Systems and their Nonlinearities. Modelling, Control and Numerical Simulation, and the kind hospitality of Carlo Lovadina (University of Pavia). |
| spellingShingle | Ortner, C Suli, E A-priori analysis of the quasicontinuum method in one dimension |
| title | A-priori analysis of the quasicontinuum method in one dimension |
| title_full | A-priori analysis of the quasicontinuum method in one dimension |
| title_fullStr | A-priori analysis of the quasicontinuum method in one dimension |
| title_full_unstemmed | A-priori analysis of the quasicontinuum method in one dimension |
| title_short | A-priori analysis of the quasicontinuum method in one dimension |
| title_sort | a priori analysis of the quasicontinuum method in one dimension |
| work_keys_str_mv | AT ortnerc apriorianalysisofthequasicontinuummethodinonedimension AT sulie apriorianalysisofthequasicontinuummethodinonedimension |