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Computational Technologies by Petr N. Vabishchevich

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Victor S. Borisov, Maria V. Vasilieva, and Alexandr E. Kolesov

11 Numerical study of applied problems

Abstract: In this chapter, we perform numerical studies of applied problems to illustrate features of the software considered above. The analysis of each problem begins with the formulation of a problem. Next, we generate the corresponding geometry and computational mesh. After that, we construct a suitable finite element discretization in space and apply an appropriate time-stepping technique for time-dependent problems using the FEniCs framework. Finally, we solve an obtained discrete problem and analyze results. Below, two-dimensional problems of melting/freezing, flow of an incompressible fluid, thermoelasticity processes, and the Joule ...

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