4 papers
A multigrid and neural network approach to reduce the computational cost of phi-FEM
Raphaël Bulle, Michel Duprez, Vanessa Lleras +1
In this work, we present a combination of a multigrid approach and the phi-FEM immersed boundary finite element method to reduce its computational cost while preserving its accurac…
A penalized ϕ-FEM scheme for the Poisson Dirichlet problem
Raphaël Bulle, Michel Duprez, Vanessa Lleras +1
In this work, we analyze a penalized variant of the ϕ-FEM scheme for the Poisson equation with Dirichlet boundary conditions. The ϕ-FEM is a recently introduced unfitted finite ele…
An adaptive multimesh rational approximation scheme for the spectral fractional Laplacian
Alex Bespalov, Raphaël Bulle
We propose a novel multimesh rational approximation scheme for the numerical solution of the (homogeneous) Dirichlet problem for the spectral fractional Laplacian. The scheme combi…
Hierarchical a posteriori error estimation of Bank-Weiser type in the FEniCS Project
Raphaël Bulle, Jack S. Hale, Alexei Lozinski +2
In the seminal paper of Bank and Weiser [Math. Comp., 44 (1985), pp.283-301] a new a posteriori estimator was introduced. This estimator requires the solution of a local Neumann pr…