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Ce cours contient les 7 premiers chapitres d'un cours d'analyse numérique donné aux étudiants bachelor de l'EPFL. Des outils de base sont décrits dans les chapitres 1 à 5. La résolution numérique d'éq
Ce cours contient les 7 premiers chapitres d'un cours d'analyse numérique donné aux étudiants bachelor de l'EPFL. Des outils de base sont décrits dans les chapitres 1 à 5. La résolution numérique d'éq
Ce cours contient les 7 premiers chapitres d'un cours d'analyse numérique donné aux étudiants bachelor de l'EPFL. Des outils de base sont décrits dans les chapitres 1 à 5. La résolution numérique d'éq
The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems).
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.
In physics, a free surface is the surface of a fluid that is subject to zero parallel shear stress, such as the interface between two homogeneous fluids. An example of two such homogeneous fluids would be a body of water (liquid) and the air in the Earth's atmosphere (gas mixture). Unlike liquids, gases cannot form a free surface on their own. Fluidized/liquified solids, including slurries, granular materials, and powders may form a free surface. A liquid in a gravitational field will form a free surface if unconfined from above.
The student will learn state-of-the-art algorithms for solving differential equations. The analysis and implementation of these algorithms will be discussed in some detail.
A mixture model to take into account the flow of small carbon dioxide bubbles dissolved in a liquid is presented. The model describes the evolution of the velocity fields (mixture and gas), the pressu
An a posteriori error estimate is derived for the approximation of the transport equation with a time dependent transport velocity. Continuous, piecewise linear, anisotropic finite elements are used f
A space-time adaptive algorithm to solve the motion of a rigid disk in an incompressible Newtonian fluid is presented, which allows collision or quasi-collision processes to be computed with high accu