UE M7-B - Scientific computing III

Level of knowledge:

N1: beginner
N2: intermediate
N3: advanced
N4: expert


Knowledge expected at the end of the course


Know how to determine the type of a partial differential equation from mechanics: hyperbolic, parabolic, elliptic. Know the paradigms of each of these types (transport, heat, Poisson): (C1, N2)


Know the derivation of distributions and the notion of weak solution of a partial differential equation: (C1,N2)


Know the basic mathematical results on linear or non-linear scalar conservation laws: Lax entropy, existence and uniqueness, finite velocity propagation, domain of dependence: (C1,N2)


Finite volume method: know how to construct a stable conservative scheme for a scalar conservation law in 1D and 2D: (C1,C2,N2)


Know how to deal with diffusion terms, source terms:(C1,C2,N2)


Know Godunov scheme, Lax-Friedrichs scheme, Lax-Wendroff scheme: (C1,C2,N2)


Know how to construct a conservative scheme for a 1D linear hyperbolic system: (C1, C2, N2)


Know the C++ programming language (and in particular object-oriented programming) for applications in scientific computing: (C3,N2)


Know how to program the solution of partial differential equations by numerical methods such as finite differences and finite volumes: (C1, C2, C3, N2).



Learning outcomes in terms of abilities, skills and attitudes expected at the end of EU courses


Analyze a hyperbolic partial differential equation with possible source and diffusion terms, its boundary conditions, and the data in order to choose an ad hoc numerical approximation (C1, C2, N2)


Construct a finite volume scheme and implement it in C++ or Fortran (C1, C2, C3, N2)


Master derivation in the sense of distributions in order to assimilate the variational methods used in the second semester for finite elements: (C1, N2)