This paper presents the basic concepts and the module structure of the Distributed and
Unified Numerics Environment and reflects on recent developments and general changes …

Abstract Partial Differential Equations (PDEs) are fundamental to model different
phenomena in science and engineering mathematically. Solving them is a crucial step …

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 develop a method for generating degree-of-freedom maps for arbitrary order Ciarlet-type
finite element spaces for any cell shape. The approach is based on the composition of …

The finite element method (FEM)(Ciarlet, 1978) is a widely used numerical method for
approximating the solution of partial differential equations (PDEs). Solving a problem using …

JuMP is an open-source modeling language that allows users to express a wide range of
optimization problems (linear, mixed-integer, quadratic, conic-quadratic, semidefinite, and …

The adjoint method provides an efficient way to compute sensitivities for system models with
a large number of inputs. However, implementing the adjoint method requires significant …

We discuss recent advances on robust unfitted finite element methods on cut meshes. These
methods are designed to facilitate computations on complex geometries obtained, for …

Firedrake is a new tool for automating the numerical solution of partial differential equations.
Firedrake adopts the domain-specific language for the finite element method of the FEniCS …

This book gives a concise and gentle introduction to finite element programming in Python
based on the popular FEniCS software library. FEniCS can be programmed in both C++ and …