7 citations · 7 across the 11 of their papers we have counts for
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Raviart Thomas Petrov-Galerkin Finite Elements
François Dubois, Isabelle Greff, Charles Pierre
The general theory of Babuška ensures necessary and sufficient conditions for a mixed problem in classical or Petrov-Galerkin form to be well posed in the sense of Hadamard. Moreov…
Rush-Larsen time-stepping methods of high order for stiff problems in cardiac electrophysiology
Yves Coudière, Charlie Douanla Lontsi, Charles Pierre
To address the issues of stability and accuracy for reaction-diffusion equations, the development of high order and stable time-stepping methods is necessary. This is particularly…
Preconditioning the bidomain model with almost linear complexity
Charles Pierre
The bidomain model is widely used in electro-cardiology to simulate spreading of excitation in the myocardium and electrocardiograms. It consists of a system of two parabolic react…
Raviart-Thomas finite elements of Petrov-Galerkin type
François Dubois, Isabelle Greff, Charles Pierre
The mixed finite element method for the Poisson problem with the Raviart-Thomas elements of low-level can be interpreted as a finite volume method with a non-local gradient. In thi…
Analysis of time-stepping methods for the monodomain model
Thomas Roy, Yves Bourgault, Charles Pierre
To a large extent, the stiffness of the bidomain and monodomain models depends on the choice of the ionic model, which varies in terms of complexity and realism. In this paper, we…