Fluid interfaces and numercial control of waves

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A first part of my research is devoted to the development and the analysis of efficient numerical methods, based on the finite element method, for the simulation of fluid flows which are interfaced with other types of media such as fluid, solid or porous media. A standard approach for the numerical computations (with the finite element method) is to build a mesh generally composed of triangles or tetrahedra. For the type of physical phenomena we are interested in, some numerical difficulties arise when the real domain has curved boundaries. Even if we can construct a mesh on a computational domain as close to the real domain as desired, the numerical computations do not necessarily tend to the "real" solution.