20 citations · 24 across the 7 of their papers we have counts for
8 papers
Distribution of distances in five dimensions and related problems
Francois Clement, Thang Pham
In this paper, we study the Erdős-Falconer distance problem in five dimensions for sets of Cartesian product structures. More precisely, we show that for wi…
The Lax-Milgram Theorem. A detailed proof to be formalized in Coq
François Clément, Vincent Martin
To obtain the highest confidence on the correction of numerical simulation programs implementing the finite element method, one has to formalize the mathematical notions and result…
First-Order Indicators for the Estimation of Discrete Fractures in Porous Media
Hend Ben Ameur, Guy Chavent, Cheikh Fatma +3
Faults and geological barriers can drastically affect the flow patterns in porous media. Such fractures can be modeled as interfaces that interact with the surrounding matrix. We p…
Trusting Computations: a Mechanized Proof from Partial Differential Equations to Actual Program
Sylvie Boldo, François Clément, Jean-Christophe Filliâtre +3
Computer programs may go wrong due to exceptional behaviors, out-of-bound array accesses, or simply coding errors. Thus, they cannot be blindly trusted. Scientific computing progra…
Image Segmentation with Multidimensional Refinement Indicators
Hend Ben Ameur, Guy Chavent, Francois Clément +1
We transpose an optimal control technique to the image segmentation problem. The idea is to consider image segmentation as a parameter estimation problem. The parameter to estimate…
Formal Proof of a Wave Equation Resolution Scheme: the Method Error
Sylvie Boldo, François Clément, Jean-Christophe Filliâtre +3
Popular finite difference numerical schemes for the resolution of the one-dimensional acoustic wave equation are well-known to be convergent. We present a comprehensive formalizati…
Formal Proof of a Wave Equation Resolution Scheme: the Method Error
Sylvie Boldo, François Clément, Jean-Christophe Filliâtre +3
Popular finite difference numerical schemes for the resolution of the one-dimensional acoustic wave equation are well-known to be convergent. We present a comprehensive formalizati…
The Multi-Dimensional Refinement Indicators Algorithm for Optimal Parameterization
Hend Ben Ameur, François Clément, Pierre Weis +1
The estimation of distributed parameters in partial differential equations (PDE) from measures of the solution of the PDE may lead to under-determination problems. The choice of a…