HALPERN , Laurence

Discrete Duality Finite Volume (DDFV) methods are very well suited to discretize anisotropic diffusion problems, even on meshes with low mesh quality. Their performance stems from an accurate reconstruction of the gradients between mesh cell boundaries, which comes however at the cost of using both a primal (cell centered) and a dual (vertex...

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We introduce a new non-overlapping optimized Schwarz method for fully anisotropic diffusion problems. Optimized Schwarz methods take into account the underlying physical properties of the problem at hand in the transmission conditions, and are thus ideally suited for solving anisotropic diffusion problems. We first study the new method at the...

Over the last five years, classical and optimized Schwarz methods with Robin transmission conditions have been developed for anisotropic elliptic problems discretized by Discrete Duality Finite Volume (DDFV) schemes. We present here the case of higher order transmission conditions in the framework of DDFV. We prove convergence of the...

We use matching asymptotic expansions to treat the antiplane elastic problem associated with a small defect located at the tip of a notch. In a first part, we develop the asymptotic method for any type of defect and present the sequential procedure which allows us to calculate the different terms of the inner and outer expansions at any order....