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Titlebook: Mathematical Modeling and Numerical Simulation in Continuum Mechanics; Proceedings of the I Ivo Babuška,Philippe G. Ciarlet,Tetsuhiko Miyos

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Can We Trust the Computational Analysis of Engineering Problems?,goals. These goals must be clearly specified. They are usually to get good qualitative or quantitative information about reality. The admissible quality of required information should be characterized.
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,Mathematical Modeling and Numerical Simulation of Earth’s Mantle Convection,rature and the phenomenon occurs in a spherical shell domain. Focusing our attention on these two factors, we describe a total approach of numerical simulation of the Earth’s mantle convection, i.e., mathematical modeling, mathematical analysis, computational scheme, error analysis, and numerical re
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Theoretical and Numerical Analysis on 3-Dimensional Brittle Fracture, of internal cracking and surface cracking in 3D elastic bodies. In Sections 2 and 3, we provide geometrical results and results on Sobolev spaces. Most criteria in fracture mechanics are based on Griffith’s energy balance theory, which is explained briefly in Section 5. .-integral is proposed by th
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Theoretical and Numerical Analysis on 3-Dimensional Brittle Fracture, however .-integral is applicable to such cases too. For practical use, we must study the combination with numerical calculation. In the last section, we give an error estimate for finite element approximation of .-integral.
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A Survey of Stabilized Plate Elements,basis functions for the deflection is one higher than that for the rotation. In the second family the stabilization is combined with the MITC interpolation technique, which enables equal order basis functions. We review the stability and error estimates which show that the methods are ”locking-free” and optimally convergent.
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