Even though nonlinear optimization seems (a priori) to be a mature field, new minimization schemes are proposed or rediscovered for modern large-scale problems. As an example and in retrospect of the last decade, we have seen a surge of first-order methods with different analysis, despite the fact that well-known theoretical limitations of the prev...
We are interested in the high-order approximation of anisotropic, potential-driven advection-diffusion models on general polytopal partitions. We study two hybrid schemes, both built upon the Hybrid High-Order technology. The first one hinges on exponential fitting and is linear, whereas the second is nonlinear. The existence of solutions is establ...
Ce travail s’intéresse à la dynamique turbulente d’un écoulement incompressible caractérisé par d’importantes variations de masse volumique, représentatif d’un rejet atmosphérique à basse vitesse. Ces écoulements sont au cœur des préoccupations du 21e siècle et leur dynamique à densité variable, qui ne peut être correctement décrite par une approxi...
In this article, high order discontinuous Galerkin methods for axisymmetric flows are developed. A first work is performed to put the equations in a so-called canonical form to gather terms of similar nature, and also for ensuring the three dimensional conservativity. Then the numerical scheme is developed. Instead of relying on the strong axisymme...
We develop and analyze error estimators and mesh adaptation strategies within a discontinuous Galerkin formulation. The basic idea of the study is to reduce the computational cost of the simulation by employing mesh adaptation as a better alternative to the use of uniform grids. The novelty of the study resides in the use of multiwavelets and how t...
With the transition to carbon-free fuels such as hydrogen, new challenges arise relating to the safe storage and transportation as well as efficient combustion of these fuels. These challenges can be better addressed by improving our understanding of the fundamental physical mechanisms controlling the dynamics of relevant combustion waves as well a...
We consider time-harmonic Maxwell's equations set in an heterogeneous medium with perfectly conducting boundary conditions. Given a divergence-free right-hand side lying in $L^2$, we provide a frequency-explicit approximability estimate measuring the difference between the corresponding solution and its best approximation by high-order N\'ed\'elec ...
We present a novel approach for high-order accurate numerical differentiation on unstructured meshes of quadrilateral elements. To differentiate a given function, an auxiliary function with greater smoothness properties is defined which when differentiated provides the derivatives of the original function. The method generalises traditional finite ...
