DOLFINx is the next generation problem solving environment from the FEniCS Project; it
provides an expressive and performant environment for solving partial differential equations …

We review different techniques to enforce essential boundary conditions, such as the
(nonhomogeneous) Dirichlet boundary condition, within a discrete variational framework …

In this work, we propose a novel formulation for the solution of partial differential equations
using finite element methods on unfitted meshes. The proposed formulation relies on the …

We introduce and analyze a penalty-free formulation of the Shifted Boundary Method (SBM),
inspired by the asymmetric version of the Nitsche method. We prove its stability and …

Extensive developments on various generalizations of the Finite Element Method (FEM) for
the interface problems, with unfitted mesh, have been made in the last few decades. Typical …

In this paper, we provide a theoretical analysis of the recently introduced weakly adversarial
networks (WAN) method, used to approximate partial differential equations in high …

We introduce a novel Fictitious Domain (FD) unfitted method for interface problems
associated with a second-order elliptic linear differential operator, that achieves optimal …

We exploit level-set topology optimization to find the optimal material distribution for
metamaterial-based heat manipulators. The level-set function, geometry, and solution field …

We present a new finite element method, called ϕ‐FEM, to solve numerically elliptic partial
differential equations with natural (Neumann or Robin) boundary conditions using simple …

We present an immersed boundary method to simulate the cree** motion of a rigid
particle in a fluid described by the Stokes equations discretized thanks to a finite element …