| Summary: | <p>The present thesis is on the error estimates of different energy based quasicontinuum (QC) methods, which are a class of computational methods for the coupling of atomistic and continuum models for micro- or nano-scale materials.</p> <p>The thesis consists of two parts. The first part considers the a priori error estimates of three energy based QC methods. The second part deals with the a posteriori error estimates of a specific energy based QC method which was recently developed.</p> <p>In the first part, we develop a unified framework for the a priori error estimates and present a new and simpler proof based on negative-norm estimates, which essentially extends previous results.</p> <p>In the second part, we establish the a posteriori error estimates for the newly developed energy based QC method for an energy norm and for the total energy. The analysis is based on a posteriori residual and stability estimates. Adaptive mesh refinement algorithms based on these error estimators are formulated.</p> <p>In both parts, numerical experiments are presented to illustrate the results of our analysis and indicate the optimal convergence rates.</p> <p>The thesis is accompanied by a thorough introduction to the development of the QC methods and its numerical analysis, as well as an outlook of the future work in the conclusion.</p>
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