This review paper discusses the developments in immersed or unfitted finite element
methods over the past decade. The main focus is the analysis and the treatment of the …

Inverse design arises in a variety of areas in engineering such as acoustic, mechanics,
thermal/electronic transport, electromagnetism, and optics. Topology optimization is an …

We present the software design of Gridap, a novel finite element library written exclusively in
the Julia programming language, which is being used by several research groups world …

Moiré superlattice patterns at the interface of two-dimensional (2D) van der Waals (vdW)
materials, arising from a small displacement between similar lattices, have been extensively …

We present Trixi. jl, a Julia package for adaptive high-order numerical simulations of
hyperbolic partial differential equations. Utilizing Julia's strengths, Trixi. jl is extensible, easy …

We propose a general framework for solving forward and inverse problems constrained by
partial differential equations, where we interpolate neural networks onto finite element …

In this work, we analyse the links between ghost penalty stabilisation and aggregation-
based discrete extension operators for the numerical approximation of elliptic partial …

Using a volumetric–deviatoric decomposition of strain, we propose a novel phase-field
model for thermo-electro-mechanical fracture and provide an open-source finite element …

In this article, we propose a novel approach for modeling brittle fracture in heterogeneous
composites using a combined diffused material interface method and a hybrid phase-field …

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 …