Many physical phenomena can be formulated as differential equations, for example the airflow around an aircraft, the evolution of a glacier or the temperature in your room. Most of these equations however can not be solved exactly by analytical tools. Their solution has to be approximated using numerical methods. The goal of this course is to implement finite element methods in 2D learned in numerical analysis course of MACS 2. That is, starting with a physical model problem, to perform and implement finite element methods to solve it, and interpret the simulations results (are the results accurate and close to the physics ?). We use the Matlab or Scilab langages first, to implement the methods in 1D. Then, you will be able to develop prototype codes with C langage, PETSc , Freefem++ and Robodoc. Once the initial problem is validate, you will be able to define relevant tests to recover the theoretical results (consistency, stability,...) studied in class. You will be able to understand problems in your calculations and deal with them.
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