6 citations · 10 across the 10 of their papers we have counts for
12 papers
Implicit and semi-implicit second-order time stepping methods for the Richards equation
Keita Sana, Beljadid Abdelaziz, Bourgault Yves
This study concerns numerical methods for efficiently solving the Richards equation where different weak formulations and computational techniques are analyzed. The spatial discret…
Mass-conservative and positivity preserving second-order semi-implicit methods for high-order parabolic equations
Sana Keita, Abdelaziz Beljadid, Yves Bourgault
We consider a class of finite element approximations for fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary vari…
Efficient second-order semi-implicit finite element method for fourth-order nonlinear diffusion equations
Sana Keita, Abdelaziz Beljadid, Yves Bourgault
We focus here on a class of fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. We design a novel secon…
Arbitrary high-order unconditionally stable methods for reaction-diffusion equations with inhomogeneous boundary condition via Deferred Correction
Saint-Cyr E. R. Koyaguerebo-Imé, Yves Bourgault
In this paper we analyse full discretizations of an initial boundary value problem (IBVP) related to reaction-diffusion equations. To avoid possible order reduction, the IBVP is fi…
Finite difference and numerical differentiation: General formulae from deferred corrections
Saint-Cyr E. R. Koyaguerebo-Imé, Yves Bourgault
This paper provides a new approach to derive various arbitrary high order finite difference formulae for the numerical differentiation of analytic functions. In this approach, vari…
Arbitrary high order A-stable and B-convergent numerical methods for ODEs via deferred correction
Saint-Cyr E. R. Koyaguerebo-Ime, Yves Bourgault
This paper presents a sequence of deferred correction (DC) schemes built recursively from the implicit midpoint scheme for the numerical solution of general first order ordinary di…
A note on the Riemann solutions to the isentropic Euler equations in the vanishing pressure limit
Sana Keita, Yves Bourgault
The behaviour of the solutions to the Riemann problem for the isentropic Euler equations when the pressure vanishes is analysed. It is shown that any solution composed of a 1-shock…
Eulerian droplet model: Delta-shock waves and solution of the Riemann problem
Sana Keita, Yves Bourgault
We study an Eulerian droplet model which can be seen as the pressureless gas system with a source term, a subsystem of this model and the inviscid Burgers equation with source term…
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…
Anisotropic space-time adaptation for reaction-diffusion problems
Edward Boey, Yves Bourgault, Thierry Giordano
A residual error estimator is proposed for the energy norm of the error for a scalar reaction-diffusion problem and for the monodomain model used in cardiac electrophysiology. The…
Anisotropic residual based a posteriori mesh adaptation in 2D: element based approach
Edward Boey, Yves Bourgault, Thierry Giordano
An element based adaptation method is developed for an anisotropic a posteriori error estimator. The adaptation does not make use of a metric, but instead equidistributes the error…
Convergence rate for the method of moments with linear closure relations
Yves Bourgault, Damien Broizat, Pierre-Emmanuel Jabin
We study linear closure relations for the moments' method applied to simple kinetic equations. The equations are linear collisional models (velocity jump processes) which are well…